The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1, 1)-block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step-size and regularization parameter. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Without doubt, the fast Fourier transform (FFT) belongs to the algorithms with large impact on science and engineering. By appropriate approximations, this scheme has been generalized for arbitrary spatial sampling points. This so called nonequispaced FFT is the core of the sequential NFFT3 library and we discuss its computational costs in detail. On the other hand, programmable graphics processing units have evolved into highly parallel, multithreaded, manycore processors with enormous computational capacity and very high memory bandwidth. By means of the so called Compute Unified Device Architecture (CUDA), we parallelized the nonequispaced FFT using the CUDA FFT library and a dedicated parallelization of the approximation scheme. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An implementation of the incomplete-LU/Cholesky preconditioned block-iterative methods on the Graphics Processing Units (GPUs) using the CUDA parallel programming model is presented. In particular, we focus on the tradeoffs associated with the sparse matrix-vector multiplication with multiple vectors, sparse triangular solve with multiple right-hand-sides (rhs) as well as incomplete factorization with 0 fill-in. We use these building blocks to implement the block-CG and BiCGStab iterative methods for the symmetric positive definite (s.p.d.) and nonsymmetric linear systems, respectively. Also, in our numerical experiments we show that the implementation of the preconditioned block-iterative methods using the CUSPARSE library on the GPU achieves an average of 3× speedup over their MKL implementation on the CPU. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we construct and analyze a two-well Hamiltonian on 2D atomic lattice considered with nonconvex interactions. Two wells of the Hamiltonian are given by two rank-one connected martensitic twins, respectively. Our combined analytical and numerical results show that the structure of ground states under appropriate boundary conditions is close to the macroscopically expected twinned configuration plus additional exponential boundary layers localized near the twinning interface. Besides, we proceed to continuum limit, show asymptotic piece-wise rigidity of minimizing sequences and derive the limiting form of their surface energy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper communicates perspectives and ideas for lengthscale-transitions for metallic materials from nano over micro to macro. For micro-macro transitions, the FE²-method is described, where a top-down perspective manifests the need to introduce even finer-scaled information than typically considered on the microscale, such as e.g. atomistic details. In contrast, the description of the Quasi-Continuum method as an atomistic-continuum transition method naturally takes the perspective of a bottom-up approach, that starts at the nanoscale and aims at larger length scales by finite element techniques. We describe the main differences between the two multiscale frameworks referring to atomistics and those which pertain to continuum mechanics. Perspectives are proposed for combining and coupling the different frameworks in a consistent way. Finally we identify fields of applications, where nanoscale information is introduced to micro-models, either via sequential/hierarchical coupling or in concurrent frameworks. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A framework for micro-to-macro transitions is developed that accounts for the effect of size at the microscopic scale. This is done by endowing the surfaces of the microscopic features with their own (energetic) structure using the theory of surface elasticity. Following a standard first-order ansatz on the microscopic motion in terms of the macroscopic deformation gradient, a Hill-type averaging condition is used to link the two scales. The surface elasticity theory introduces two additional microscopic length scales: the ratio of the bulk volume to the energetic surface area, and the ratio of the surface and bulk Helmholtz energies. The influence of these microscopic length scales is elucidated via a series of numerical examples performed using the finite element method. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Understanding of micromechanical mechanisms in functional materials with electro-mechanical coupling is a highly demanding area of simulation technology and increasing interest has been shown in the last decades. Smart materials are characterized by microstructural properties, which can be changed by external stress and electric field stimuli, and hence find use as the active components in sensors and actuators. In this context, a key challenge is to combine models for microscopic electric domain evolution with variational principles of homogenization. We outline a variational-based micro-electro-elastic model for the micro-structural evolution of electric domains in ferroelectric ceramics. The micro-to-macro transition is performed on the basis of variational principles, extending purely mechanical formulations to coupled electro-mechanics. We focus on an electro-mechanical Boltzmann continuum on the macro-scale with mechanical displacement and electric potential as primary variables. The material model on the micro-scale is described by a gradient-extended continuum formulation taking into account the polarization vector field and its gradient, see Landis [1] and Schrade et al. [2] for conceptually similar approaches. A crucial aspect of the proposed homogenization analysis is the derivation of appropriate boundary conditions on the surface of the representative volume element. In this work we derive stiff Dirichlet-type, soft Neumann-type, and periodic boundary constraints starting from a generalized Hill-Mandel macrohomogeneity condition. Furthermore, we propose techniques to incorporate these boundary conditions in the variational principles of homogenization by means of Lagrange multiplier methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For a phase field model, which consists of the elasticity equations coupled to the Allen-Cahn equation, we state an asymptotic expansion for the propagation speed of the diffusive interface. The error of the expansion is of order η², where η is the width of the interface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We use the principle of maximum dissipation for thermo-mechanically coupled modeling of poly-crystalline shape memory alloys (SMA). This modeling scheme demands approaches for both Helmholtz free energy and dissipation. For time-independent processes, dissipation is usually modeled by the norm of the internal variable's rate times a factor. We show that for SMAs this factor is not an additional modeling parameter. In contrast, it can be calculated from the Helmholtz free energy. This reduces the number of model parameters and provides furthermore an interesting effect of the model which allows to display the material behavior in an even more realistic manner. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The macroscopic mechanical behavior of many materials crucially depends on the formation and evolution of their microstructure. In this work, we consider the formation and evolution of laminate deformation microstructure in plasticity. Inspired by work on the variational modeling of phase transformation [5] and building on related work on multislip gradient crystal plasticity [9], we present a new finite strain model for the formation and evolution of laminate deformation microstructure in double slip gradient crystal plasticity. Basic ingredients of our model are a nonconvex hardening potential and two gradient terms accounting for geometrically necessary dislocations (GNDs) by use of the dislocation density tensor and regularizing the sharp interfaces between different kinematically coherent plastic slip states. The plastic evolution is described by means of a nonsmooth dissipation potential for which we propose a new regularization. We formulate a continuous gradient-extended rate-variational framework and discretize it in time to obtain an incremental-variational formulation. Discretization in space yields a finite element formulation which is used to demonstrate the capability of our model to predict the formation and evolution of laminate deformation microstructure in f.c.c. Copper with two active slip systems in the same slip plane. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper deals with aspects on the dynamic modulation of the robots mechanical structure, using Lagrangian formalism, choosing the adequate DC servomotors, translation modules constituting the TTRT robot, the constructive solution and modelling the three translation subassemblies of the studied robot, with the intention that, in the end, based on a dynamic-organologic algorithm, a functional optimization of the robot be brought out within a workcell destined for special applications, so that the energetic consumption be as low as possible. This paper also presents the organological calculi and solutions for the efficient design of modules specific to mechanical structures of industrial serial-modular robots. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The results of this work appeared in the process of studying a certain problem on the rigid body motion in a medium with resistance, where we needed to deal with first integrals having nonstandard properties. Precisely, they are not analytic, not smooth, and on certain sets, they can be even discontinuous. Moreover, they are expressed through a finite combination of elementary functions. However, the latter circumstances allowed us to carry out a complete analysis of all phase trajectories and show those their properties which have a “roughness” and are preserved for systems of a more general form having certain symmetries of latent type. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Based on Lie groups theory, this work considers the problem of decomposition of a given rotation into three successive finite rotations with prescribed in advance axes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The mechanical behaviour of molecular structures can be described with stiff differential equations, which can not be solved analytically. Several numerical time integration schemes can be found in the literature. The aim of this paper is to present the class of partitioned Runge-Kutta methods applied in molecular dynamics. This class of methods includes a wide range of explicit and implicit, single- and multi-stage, symplectic and non-symplectic, low- and high-order time integration schemes. Also most of the classical methods like explicit and implicit Euler, explicit and implicit midpoint rule, Störmer-Verlet and Newmark are also partitioned Runge-Kutta methods.

The schemes are implemented in a finite element code which can serve as a numerical platform for molecular dynamics. This code is used to show the sensitivity of the simulations to the accuracy of the initial values. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A Discrete Element Model that is capable to describe degradation of ballast tracks in consideration of breakage of the ballast stones is presented. Strong rock is modelled as a granular solid by introduction of breakable bonds with suitable failure criteria between adjacent particles. Irregular angular stones are generated from the granular solid and their crushing strength is evaluated. The degradation process of a ballast bed is assessed and related to the damage occurring to the individual stones. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of this paper is to present the results of the investigations of the ability of self-excited vibrations due to friction in a planar simplified mechanical model, with a constant coefficient of friction. The Hurwitz criteria is used for the stability analysis and the determination of the critical value of the coefficent of friction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Strong crosswind gusts have great influence on the stability of railway and road vehicles. They may lead to accidents and also to a discomfort for the road vehicle driver. Risk assessment for overturning of railway and road vehicles is usually calculated based on the stationary situation or at least on wind-tunnel experiments that are mostly carried out with a static vehicle model. Nonstationary excitation due to wind turbulence occurs if the vehicle accelerates or decelerates. Increasing vehicle speed relative to wind speed will move the energy content of the spectrum to a higher frequency range. It has been realized that nonstationary wind has a great influence on vehicle stability especially when the vehicle speed is high. Thus in order to assess the overturning risk in a more realistic way, a nonstationary wind model together with its interaction with the vehicle should be taken into consideration.This paper proposes a nonstationary wind turbulence model for the investigation of crosswind stability of ground vehicles. A wind model with nonstationary turbulence as well as the wind effects to the moving vehicle in a nonstationary situation (acceleration/deceleration) is described. Nonstationary aerodynamic forces are considered together with the interaction between the moving vehicle system and the wind turbulence. Failure probabilities are computed and reliability analyses are carried out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the past, a lot of effort has gone into the development of structure-preserving time-stepping schemes for forward dynamic problems. This is due to the superior numerical stability of these integrators. Guided by previous developments in the design of energy-momentum integrators for forward dynamic problems, a Hamiltonian conserving indirect optimal control method will be introduced. For the state equations, a consistent variant of the midpoint evaluation introduced in [1] will be applied. Based on this specific discretization of the state equations, a discretization of the costate equations will be introduced, which is based on the notion of a discrete derivative and which leads to the algorithmic conservation of the discrete Hamiltonian. The newly developed method will be compared with a direct transcription method. We will test the newly proposed method within two numerical examples, which are the optimal control of a particle in a gravitational field and a 3-link manipulator. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution introduces and illustrates the concept of fuzzy arithmetic as a modeling and analysis tool for the simulation of multibody systems subjected to uncertainties. The uncertainties are described by the use of fuzzy numbers and the simulation procedure is performed by employing the Transformation Method, which is a practical methodology for the implementation of fuzzy arithmetic. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The main goal of the present work is to provide an add-on scheme for the formulation of multibody dynamics, based on natural coordinates, in regard to ideally balanced rigid bodies with high rotational spin, e.g. gyroscopes. The underlying aim of this approach is to achieve higher numerical accuracy whenever the preferred axis of rotation coincides with the balanced main axis of the body. This will be achieved by seperating the spin of the balanced rigid body along the denoted axis as an additional angular coordinate, whereas the other rotations will be covered by a carried frame, parameterized via natural coordinates. At the same time the carried frame provides a link to the existing modelling framework in terms of natural coordinates, enabling a straightforward implementation into existing multibody systems (e.g. rotary crane [2]). (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Natural coordinates have emerged to be well-suited for both rigid and flexible multibody dynamics. Especially the combination of structural elements and energy-momentum consistent time stepping schemes leads to superior numerical stability as well as an automatable assembly, resulting in both excellent run-time behaviour as well as moderate modelling effort (see [1]). Incorporation of modern methods for finite-element simulations, such as mortar methods for contact or domain decomposition both for structural elements as well as continuum elements is straightforward ([2]).

Augmentation techniques allow a systematic integration of both mechanical and non-mechanical quantities for simulation (see [3] and [4]), which makes this approach suitable especially for emulation and simulation of mechatronic systems. We will present an approach for evaluating forward control strategies with flexible multibody systems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Control constraints can be used to prescribe the motion in the inverse dynamics of multibody systems. If the number of control inputs is lower than the degrees of freedom, this kind of mechanical system is called underactuated system. The solution of such partly specified system is a challenging task due to the underactuation property. The description of underactuated systems can be based on either minimal coordinates or redundant coordinates. The resulting governing equations show the form of differential-algebraic equations (DAEs) with a mixed set of holonomic and control constraints. The index of the DAEs may exceed three and alternative projection methods will be applied to reduce the index to three. Numerical examples are used to compare the alternative projection methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastomerbauteile in Fahrwerken dienen der gezielten Beeinflussung der Gesamtelastokinematik. Im Entwicklungsprozess versucht der Konstrukteur die optimale Lösung für den jeweiligen Anwendungsfall zwischen Fahrdynamik inbesondere bei Kurvenfahrt und Fahrkomfort zu finden. Zusätzlich wird in diversen Achskonstruktionen diesen Bauteilen eine die Fahrzeugsicherheit beeinflussende Funktion überlassen. Die Kenntnis des komplexen Bauteilverhaltens, inbesondere der mechanischen Wechselwirkungen, ist daher wünschenswert. Mit einer Kombination aus Finite-Elemente-Analysen und der Mehrkörpersimulation können diese Effekte untersucht werden. An einem Beispiel aus der Fahrzeugdynmaik wird gezeigt, in welcher Größenordnung sich der Einfluss der Wechselwirkungen auf das Fahrverhalten bewegen kann. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Lightweight techniques are applied increasingly often for modern machine designs in order to reduce the moving masses and therewith the energy consumption. However, as a result the stiffness of the system decreases causing undesired elastic deformations and therewith end-effector deviations. In this work a topology optimization procedure for elastic multibody systems based on the solid isotropic material with penalization approach is presented to lower end-effector tracking errors. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The application process of active anti-roll systems can be supported by the implementation of numerical optimization routines. The optimization objectives evaluate the handling and comfort vehicle behaviour and are calculated online from vehicle measurement variables. A model-based analysis illustrates the influence of the actuator properties on these optimization objectives. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work considers the structure preserving simulation of three-dimensional multibody dynamics with contacts. The used variational integrator is based on a discrete version of the Lagrange-d'Alembert principle, which yields a symplectic momentum method. One of our main goals is to guarantee the structure preservation and the geometric correctness, thus we solve the non-smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non-smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a finite dimensional constrained optimisation problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In multibody systems, two alternative approaches exist to compute contact forces between bodies. The unilateral constraint contact and the unilateral regularized contact do not take into account the influence of the deformation due to other contacts on a body using rigid body dynamics. In this paper, a third alternative, i.e. the Maxwell-Contact, is derived coupling the deformations of different contacts on one body quasi-statically. An academic example validates the fundamental properties of the contact model and the application in a simulation of a pushbelt CVT shows improved results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper introduces the kinematical and dynamical model as well as a quasi-static trajectory control of a self-balancing two-wheeled vehicle. The mobile robot is about 60cm tall, autonomous, unstable and driven by two wheels. Hence, it can be used for transport purposes. Due to the nonholonomic constraints only few modeling techniques are feasible. In this case, the modeling is based on the Projection Equation, followed by the derivation of various control strategies.

In order to allow a desired velocity and to stabilize the inclination angle of the robot a partial feedback linearization in combination with a LQR controller is applied. The quasi-static trajectory controller, which is based on the kinematical model, uses a flatness based approach in order to remain on the desired path. Continuous curvature paths, composed by clothoids, enable good performance results in simulation and experiment. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In previous works, discrete mechanics and optimal control for constrained systems (DMOCC) has been introduced for the structure preserving simulation of optimal control problems for rigid multibody systems, whereby possible contacts or collisions between the bodies have been disregarded. In the formulation presented here, both collision avoidance as well as explicitly planned collisions between non-smooth bodies are included. To this end, a subdifferentiable global contact detection algorithm, the supporting separating hyperplane linear program (SSHLP), based on the signed distance between supporting hyperplanes of two convex sets, is used in the simulation of optimal control problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

If one is dealing with active vibration suppression on a highly nonlinear flexible system, various techniques are needed. On the one hand a suitable dynamic model of the system is required. And on the other hand intelligent model based control concepts are necessary for active vibration damping. We deal with a basic model, where the flexibilities are approximated with linear springs and dampers, a so called lumped element model (LEM). For the control design we propose a control structure with two degrees of freedom (2DoF) for solving the tracking problem, based on the LEM. Such an approach allows designing the feedforward part independently of the feedback part. Hereby the feedforward control is based on the flatness approach, while for the feedback control several strategies are studied using acceleration- and gyrosensor-measurements. The contribution is completed with a validation by measurements from a very fast trajectory on an articulated robot with two flexible links and three elastic joints. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Coupling different subsystem simulators can be accomplished by a co-simulation [1, 2]. For this purpose, the subsystem solvers are coupled by appropriate input and output variables. In order to analyze the stability of the coupled simulation, not only the coupling technique must be taken into account, but also the subsystem integrators. On the one hand, the stability of the co-simulation is influenced by the extrapolation of the coupling variables and by the macro-step size. On the other hand, the numerical errors arising from the subsystem solvers may directly affect the coupled simulation. The focus of this paper lies on the question, how the subsystem solvers influence the co-simulation. Therefore, numerical studies regarding the numerical stability and the convergence order have been carried out by using a co-simulation test model. We restrict ourselves to explicit co-simulation techniques, based on a zero-stable applied-force coupling approach. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper addresses the dynamical modeling and control of reconfigurable modular robots. The modular actuators (brushless DC motors with Harmonic Drive gears) for the robots under consideration are connected by rigid links. This way the robot can be assembled in different configurations by rearranging these components. For dynamical modeling the Projection Equation in Subsystem representation is used, taking advantage of its modular structure. Due to the lack of position sensors at the gearbox output shaft, deflections caused by the elasticities in the gears can not be compensated by the PD motor joint controller. Therefore, a correction of the motor trajectory is needed, which can be calculated as part of a flatness based feed-forward control using the exact model of the robot. With the recursive approach proposed in this paper the concept of reconfigurability is retained. For validation a redundant articulated robot arm with seven joints is regarded and results are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper a new class library for the computation of the forward multi-body-system (MBS) dynamics of robots and biomechanical models of human motion is presented. By the developed modular modeling approach the library can be flexibly extended by specific modeling elements like joints with specific geometry or different muscle models and thus can be applied efficiently for a number of dynamic simulation and optimization problems. The library not only provides several methods for solving the forward dynamics problem (like articulated body or composite rigid body algorithms) which can transparently be exchanged. Moreover, the numerical solution of optimal control problems, like in the forward dynamics optimization of human motion, is significantly facilitated by the computation of the sensitivity matrix with respect to the control variables. Examples are given to demonstrate the efficiency of the approach. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of the present work is to investigate the remodeling phenomenon of a cell-seeded tissue. In experiments, a cell seeded condensed collagen gel is mechanically stimulated in a bioreactor for four weeks, after which the specimen is tested in compression to measure its change of stiffness. The change, regarded as remodeling, is assumed to be the result of newly synthesized collagen type II; a constitutive equation is proposed for the remodeling effect. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The here presented 3D-FEM model describes of microperfusion in liver lobules with the main focus on the remodeling of the microperfusion after a hepato-venous outflow obstruction caused for example by liver resection. Via a dilatation and reorientation of small vessels within the lobule, the so called sinusoids, a connection between the obstructed and normal drained areas is established. For the remodeling of the microperfusion the phenomenological approach, namely that the reorientation of the sinusoids mainly depends on the blood pressure gradient, is applied. A biphasic homogenized approach within the framework of the theory of porous media (TPM) is chosen for the modeling of the microperfusion. This work sums up the constitutive equations for the biphasic model regarding the filter velocity and transversely isotropic permeability depending on our phenomenological approach. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution a coupled material framework is presented, which considers the effects of damage and growth in soft biological tissues. The tissue is described as a porous medium by taking into account a solid and a fluid phase. The fluid phase is assumed to carry nutrients supplying growth of the solid phase. The latter one is described as a fiber-reinforced material, where a damage variable is introduced for the fiber part of the associated free energy function. The performance of the proposed model is demonstrated in a finite element analysis of a simplified human heart model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present study the anisotropic mechanical properties such as elasticity and diffusion of bovine Bruch's membrane (BM) and a collagen foils (CF) are compared with each other. For this reason, a constitutive material law is developed and implemented into a FEM software. Based on tensile tests, the material parameters of both materials are identified. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Soft tissues are commonly applied in surgery to replace the injured articular cartilage. Many biological researches were carried out through mechanical and histological experiments. They focus on the function, degeneration and regeneration of the articular cartilage and fibrocartilage. The aim of the presented work is to develop a method to characterize the mechanical properties of different kinds of soft tissues and to trace the evolution of elastic properties in implants during the remodeling process. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The effects of damage of intervertebral discs on their biomechanical behaviour and the factors favouring the progression of instability are studied. Healthy and damaged movement segments are analyzed experimentally and numerically. The aim is to represent and predict the effects of tissue damage and changes in the spine by comparison with healthy segments. Since the intervertebral disc acts as a mechanical damper, relaxation tests are performed in addition to pressure experiments. The experiments are carried out in a bioreactor with tempered nutrient solution. A cultivation period in the bioreactor allows detecting cell viability, solute diffusion rates and gene expression of the discs. Numerically, the nonlinear, viscoelastic, anisotropic and diffusion-dependent behaviour of the intervertebral disc is modelled with the FE-program Abaqus, using a modular material law as a UMAT subroutine. With the measurement results, the relevant parameters can be determined so that the mechanical behaviour of intervertebral discs can be simulated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Using multibody systems to represent bones and joints is a common way to simulate human motion. Often, this is done with inverse or forward dynamics (solving initial value problems). However, many simulation tasks in biomechanics lead to boundary value problems, like performing a motion from a given start to a prescribed end position, which could be performed in various ways. In this context, we suppose that human motion is controlled in order to perform an optimal motion. Hence we formulate an optimal control problem (OCP) and compare the results when using different physiologically motivated cost functions. A direct transcription method called DMOCC (see [1]) is used to solve the OCP, whereby we benefit from it's structure preserving formulation, as the resulting optimal discrete trajectories are symplectic-momentum preserving. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Parameters of material models are commonly identified by fitting predicted stress-stretch relations to experimentally derived ones, assuming homogeneous deformation. This approach has been compared with an inverse finite element strategy, where an FE model of the actual measurement set-up is created to obtain stress-stretch data. Compressive tests of skeletal muscle tissue have been conducted for different fiber orientations, with a stereo camera system capturing the geometry of the sample. The material exhibited an exponential increase in stiffness with increasing stretch, with large differences related to the fiber orientation; this behavior is described well by a model for arterial layers. Assuming homogeneous deformation led to significantly different stress-stretch curves indicating that this assumption is unrealistic in this case. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Percutaneous vertebroplasty is a common clinical procedure to treat vertebral compression fractures and osteoporotic vertebral bodies. However, this operation technique is accompanied by different complications due to lack of knowledge about the complicated behaviour of bone cement within the human body. To contribute to a better understanding of the processes that take place inside the body during a vertebroplasty, a detailed model of the thermomechanical behaviour of acrylic bone cement has been developed. All important effects are covered, that influence the behaviour of acrylic bone cement during the injection in a human vertebral body. Implemented in the opensource CFD-code OpenFOAM^®, first results show that this comprehensive simulation of the minimal invasive injection is capable to accurately predict the cement distribution and temperature field of acrylic bone cement inside the vertebral body. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Articular cartilage is a viscoelastic, two-phase and fiber-strengthen tissue; it consists of a solid and a fluid phase. We describe this tissue using the Theory of Porous Media (TPM). Some simulation results are shown. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A direct intracranial infusion of a therapeutic solution into the extra-vascular space of human brain tissue is a promising medical application for the effective treatment of malignant brain tumours [1]. The advantage of this method, compared to an intra-vascular medication, is the targeted delivery with the circumvention of the blood-brain barrier (BBB), which prohibits the passing of therapeutic macro-molecules across the vascular walls into the brain parenchyma.

The prediction of the resulting therapeutical distribution by a numerical simulation is challenging, since the spreading is affected by the complex nature of living brain tissue. For this purpose, a macroscopic continuum-mechanical model is established within the Theory of Porous Media (TPM), proceeding from a homogenisation of the underlying micro-structure [5]. The ternary four-component model consists of an elastically deformable solid skeleton (composed of tissue cells and vascular walls), which is perfused by two mobile but separated liquid phases, the blood and the overall interstitial fluid (treated as a real two-component mixture of the liquid solvent and the dissolved therapeutic solute). The strongly coupled solid-liquid-transport problem is simultaneously approximated in all primary unknowns using mixed finite elements (uppc-formulation) and consequently solved in a monolithic manner with an implicit time-integration scheme.

This numerical investigation allows the computational study of several circumstances influencing the irregular distribution of infused drugs, as observed in clinical studies. Therefore, the microstructural perfusion characteristics in the extra-cellular space of the white-matter tracts are considered by a spatial diversification of the anisotropic permeability tensors, provided by Diffusion Tensor Imaging (DTI). Furthermore, Magnetic Resonance Angiography (MRA) enables the in vivo location of blood vessels within the brain tissue. Finally, the selection of appropriate material parameters has a crucial influence on the drug distribution profile and further occurring effects beyond. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work introduces a modelling framework towards a forward dynamics simulation of skeletal muscle mechanics that couples three-dimensional (3D) continuum-mechanical-based Finite Element (FE) simulations to rigid body simulations. In this regard, this is a methodological approach, which incorporates different methods to realise simulations of the musculoskeletal system. Such simulations are at present computationally not feasible.

To set up such a modelling framework the upper limp is selected. Here, the upper limb consists of an antagonistic muscle pair, the elbow (a simple hinge joint) and an external load. The skeletal muscles are represented by a 3D continuum-mechanical model. The tendons are, for now, assumed to be rigid. The results demonstrate the ability of the system to converge to a physiological realistic position. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The main sources of noise at work, in industrial environments, are machine tools: namely, mechanical transmission structure composed of gears, bearings, electric motors drive and the cutting process. Generated vibrations are transmitted through structures, carcasses or directly to environment, developing a complex acoustic field around machine tools. In terms of occupational medicine, the noise is generated by a combination of vibrations producing sounds with different characteristics and that are produced in the workplace [2]. It is important to identify the dominant noise source, the cause of exceeding the admissible limits (87dB) and noise transmission mode to make an objective correlation with effects on humans [1]. Hearing loss can occur immediately at extreme sound levels, but, in general, the problem is noise exposure over time. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper will be a short presentation of the specialized literature and international standards about the importance of vibration action of portable machine tools on human body and particularly on the hand-arm system. Exposure to harmful vibrations can lead to health problems and disorders, especially in the upper joints and dorsal region of the human body. A detailed understanding of the undesirable effects of vibration on the human body is essential to achieve administrative and technical prevention. In modern times, vibration studies become more frequent, decisive for the many machines, vehicles and construction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Work includes identifying and analyzing vibrations produced by a trilling machine MA750 within space work. To identify vibration is used a special method, which has not been used so far in identifying vibrations, with the action on the human body. For obtaining a very good identification of the human body vibrations has been used the Moiré projection method. General conditions were applied to human hand operator during working hours on a trilling machine, with different speeds of main shaft. In the paper are presented successively two methods of measuring the vibrations: the Moiré projection method and conventional method of measuring the vibrometer. The results in the booth situation (classical measurements and Moiré projection method) were in the same order of the unit scale, and the optical method named Moiré projection method can be considered a valid method for the human vibrations measurements without touch of the surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A multi-scale and multi-physics geometrical model of skeletal muscle is presented. Therein, the excitation-contraction pathway is described by a biophysical cell model of systems biology; the propagation of action potentials along individual muscle fibres is represented by means of the monodomain equation; a continuum-mechanical description of the mechanical behaviour of the entire muscle is employed that relies on an additive split of the second Piola-Kirchhoff stress tensor.

Opposed to previous models, the multi-physics problem is solved simultaneously using a staggered solution scheme that allows for a multi-directional coupling between the different physical phenomena, and a parallel implementation is used. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present study is aimed at a physically based mechanical model for prosthetic meshes at the mesoscale. The geometry and the local kinematics of a representative unit cell are mapped in an abstracted, but still physically relevant description. Such a model allows to understand the interplay between local deformation patterns and the resulting global anisotropic and nonlinear force response. It is expected to provide design criteria for mesh implant optimization, not only accounting for the global mechanical behavior but also for local mesh-tissue interactions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We focus in this work on isotropically growing materials. An adaptive algorithm is used in order to maintain a stress-free state during growth if no external loads are applied, but keeping the volume growth defined by a former kinetic. The proposed model is based on a modified multiplicative split of the deformation gradient into a growth part and an elastic part. The growth part will be isotropic if the elastic deformations are favourable, otherwise the growth will find a more comfortable direction. Three-dimensional examples based on different kinetics are presented and discussed using the numerical model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present a constitutive model for microbial biofilms with application to biofilms of Pseudomonas aeruginosa whose EPS contain large amounts of alginate. The EPS matrix is modelled as a transient network of worm-like chains with different types of junctions. The implementation as a nearly incompressible material allows large strain finite element calculations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Aim of this work is to obtain a convenient data set for the validation of a recently developed three-dimensional constitutive muscle model. Therefore, an optical measurement technique is used to reconstruct a geometrical model of a rabbit soleus muscle. Thus, the muscle geometry and also the generated force characteristics are measured. The proposed numerical model is able to reproduce the experimental results in an adequate manner. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Up to now, the interaction mechanisms between cartilage and synovial fluid within diarthrodial joints are not fully understood. These joints are able to function effectively over the lifetime of an individual even under very high loads, which requires minimal wear of cartilage. In particular, the reason for the extremely low coefficients of friction has still to be explained.

The goal of this contribution is to numerically investigate the interaction between articular cartilage and synovial fluid in diarthrodial joints. In this connection, we already developed an appropriate continuum model of the articulating tissue layers as highly anisotropic and heteregeneously charged biphasic solid-fluid aggregates based on the Theory of Porous Media (TPM). The calibration of the previously elaborated model is the next concern. To this end, a sensitivity analysis is performed to identify the relevant constitutive parameters governing the cartilage response during indentation tests. The remaining parameters are then estimated numerically using a direct search algorithm. Next, a sequential solution algorithm has to be developed in order to solve the complex contact problem at the interface between synovial fluid and articular cartilage. Thereby, the fluid and cartilage domains are iteratively calculated until equilibrium is reached. For the moment, simulations are performed on a 3-d hip-joint geometry reconstructed from MRI data, which proceed from a continuum-mechanical description of the synovial fluid gap. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the context of the Theory of Porous Media (TPM), a continuum-mechanical model is introduced to describe the complex fluid-structure interaction in bone tissue on the macro-scale. The tissue is treated as an aggregate of two immiscible constituents, where the cells and the bone matrix are summarised to the solid phase, and the fluid phase summarises the extracellular fluids and their components. The remodelling process is described on the macro-scale by a distinct mass exchange that also causes a change of the constituents' material properties. In addition to the mechanical description, systems-biological control mechanisms are included into the model by evaluating a systems-biological cell interaction model at every integration point of the spatially discretised domain.

Here, an integrative solution strategy is presented for this combined mechanical and systems-biological problem. Therein, the mechanical problem is treated using the Finite-Element Method (FEM), where the systems-biological problem is solved locally on integration point level in the sense of a collocation method. To reveal the whole capability of this approach, a 3-dimensional numerical example of the remodelling process in the upper human femur under physiological loading conditions is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work focuses on the development of new finite elements which can capture strong discontinuities in three-dimensional failure problems. The displacement jumps in the solid are approximated by a linear interpolation obtained by enforcing a new class of enhanced separation modes to exactly be satisfied by the formulation. Efforts are also put towards the development of a proper crack propagation tracking algorithm needed for the complicated crack surfaces appearing in realistic 3D failure simulations, based on a combination of the global tracking algorithm and the marching cubes algorithm. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The current work presents the multilevel approach of the embedded finite element method which is obtained by combining features of the method of domain decomposition with those of the standard embedded finite element method. The conventional requirement of fine mesh in a possible failure zone is rendered unnecessary with the new approach thereby reducing the computational expense. In addition, it is also possible to stop a propagating crack-tip in the middle of a finite element. In this approach, the finite elements at the failure-prone zone where cracks or shear bands, referred to as strong discontinuities which represent jumps in the displacement field, can form and propagate based on some failure criterion are treated as separate sub-boundary value problems which are adaptively discretized during the run time into a number of sub-elements and subjected to a kinematic constraint on their boundary. Each sub-element becomes equally capable of developing a strong discontinuity depending upon its state of stress. A linear displacement based constraint is applied initially which is modified accordingly as soon as a strong discontinuity propagates through the boundary of the main finite element. At the local equilibrium, the coupling between the quantities at two different levels of discretization is obtained by matching the virtual energies due to admissible variations of the main finite element and its constituent sub-elements. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The problem of ductile damage and failure prediction at the upsetting of cylindrical specimens with artificial voids is solved by taking a change in stress triaxiality into account. It is shown that such a more accurate assessment leads to a greater shift of stress triaxialities into a range of negative values as compared to their averaged values. At such values of stress triaxiality the material can be subjected to compression without failure under arbitrarily large deformations due to healing of micro-defects. The constitutive equations of a recently developed tensorial framework for ductile damage [5] are applied to modelling. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The damage process of metal-ceramic functionally graded material (FGM) is investigated. The microcrack evolution in a layered structure is analyzed using a numerical simulation of stresses and configurational forces. The modelling of an FGM of alumina ceramic and a metallic phase with gradually changing volume fraction of alumina is performed. A structure of two different layers bonded to a substrate is simulated. The stiffness and density of the three materials are varying. The evolution of configurational forces is simulated. The influence of the crack length on the crack driving force is studied for the case of a stress wave loading. The stress loading is applied in the horizontal direction as a dead load. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A method for crack detection and stress intensity factor measurement in plate structures is presented by using strain gauges and applying the Body Force Method (BFM). The BFM is based on elastic solutions for concentrated loads and the principle of linear superposition allowing e.g. the calculation of the strain field in a cracked body. The inverse problem is solved applying the PSO (particle swarm optimization) and the unknown parameters are crack position, length and inclination as well as loading quantities. Experiments are carried out under cyclic loading using pre-cracked plates made of aluminum alloy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present study is concerned with the investigation of the micro mechanisms of micro defect nucleation in bainitic steels in order to provide an enhanced basis for probabilistic cleavage models. By a micro mechanical modelling of the cleavage initiation process the effects and the interactions of the relevant parameters can be identified. For this purpose Representative Volume Elements (RVE) of the micro structure are utilised, accounting for both, the grain structure as well as the brittle particles at the grain boundaries. The RVE's are loaded based on the local mechanical field quantities determined numerically at the cleavage origins of different fracture mechanics specimens. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The singular edge-based smoothed finite element method (sES-FEM) is developed for stationary dynamic crack analysis in two-dimensional (2D) elastic solids. The paper aims at providing a better understanding of the dynamic fracture behaviors in linear elastic solids by means of the strain smoothing technique. The strains are smoothed and the system stiffness matrix is performed using the strain smoothing over the smoothing domains associated with the element edges. A two-layer singular five-node crack-tip element is employed while the standard implicit time integration scheme is used for solving the discrete sES-FEM equation system. Dynamic stress intensity factors (DSIFs) are extracted using the domain-form of interaction integrals in terms of the smoothing technique. The normalized DSIFs are compared with reference solutions showing a high accuracy of the sES-FEM. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present contribution the authors applied numerical homogenization techniques to predict the effective material behavior of composite based on the simulation of a representative volume element (RVE) [1]. An enriched displacement approximation (XFEM) is used to describe weak and strong discontinuities within the displacement field, independent from the underlying FE mesh. For the description of curved material interfaces a higher order XFEM formulation based on quadratic shape functions and consisting integration sub domains is developed. In order to incorporate microscopic damage effects, the XFEM approximation has been combined with a cohesive zone approach to model failure of the fiber-matrix interface. The inelastic properties of the polymeric matrix material are described via constitutive relations of fractional viscoelasticity with process dependent viscous properties. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work investigates gradient-enhanced damage evolution by performing a parameter study for the authors's finite element shell model [1], in which the free energy function is enhanced phenomenologically in terms of a non-local damage variable and its gradient on the mid-surface of shell structures. This enhancement gives rise to an introduction of gradient parameters in terms of a substructure-related intrisic length-scale and a relationship between non-local and local damage variable. Based on the global displacement-force curves obtained from shock-tube tests on aluminium plate specimens, the gradient parameters are determined to validate the proposed shell model. The influence of spatial gradient of loading on the material behaviour within a macroscopic continuum element will be discussed through several examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In micro-electronic materials such as solder alloys, phase-separation and coarsening as well as damage phenomena occur at the same time and influences each other. In this note, a unifying model which couples multi-component Cahn-Hilliard systems with elasticity and uni-directional damage processes is presented. We outline the equations and their initial-boundary conditions in a classical setting and cite some existence results for weak solutions recently proved in [8, 9]. The damage is assumed to be incomplete, i.e. the maximal damaged material parts still feature elastic properties. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Previous studies on the sensitivity of cracks in ice shelves with different boundary conditions, stress states and density profiles revealed the need for further analyses. As the transfer of boundary conditions from dynamic ice flow simulations to the linear elastic fracture analyses proved to be a critical point in previous studies, a new approach to relate viscous and elastic material behaviour is proposed. The numerical simulations are conducted using Finite Elements utilizing the concept of configurational forces. To show the applicability of the approach, a 2-dimensional plane stress geometry with volume loads due to the ice shelf flow is analyzed. The resulting crack path is compared to available crack paths from satellite images. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An incremental variational formulation for damage at finite strains is proposed based on the classical continuum damage mechanics. Since loss of convexity is obtained at some critical deformations a relaxed incremental stress potential is constructed which convexifies the original non-convex problem. The resulting model can be interpreted as the homogenization of a micro-heterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one-dimensional relaxed formulation is derived and based thereon, a model for fiber-reinforced materials is given. Finally, some numerical examples illustrate the performance of the model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work presents numerical methods used for predicting crack paths in technical structures based on the theory of linear elastic fracture mechanics. The FE-method is used in combination with an efficient remeshing algorithm and a post processor to calculate crack tip loading. The interaction of cracks and internal boundaries and interfaces is investigated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Phase field fracture models typically feature a length parameter, which controls the width of the diffuse transition zone between broken and undamaged material. In the limit case of a vanishing length parameter, these models converge to a sharp crack formulation. From this point of view, the length scale parameter is a purely auxiliary numerical quantity. However, the study of the stability of homogeneous solutions in a one dimensional setting permits a different interpretation. Since the length parameter is directly related to the critical stress at which the homogeneous solution becomes unstable and crack nucleation occurs, it can be related to the strength of the material. In this regard, the length parameter itself may be seen as a material parameter. These analytical findings are approved by finite element simulations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper the research results of hybrid composite materials made of a steel plate and laminates are presented. The tested composites were made of a metal sheet plate and a laminate plate connected by means of barbed studs. The laminates were made of three different types of fabrics with: fibreglass, carbon fibres and aramid fibres. As a warp, epoxide resin and polyester resin were used. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the study interface cracks between two dissimilar homogeneous isotropic half-spaces undergoing impact loading are considered. The problem is solved using the boundary integral equations in the frequency domain. The distributions of the displacements and tractions at the bonding interface and surfaces of the cracks are obtained and analyzed. The stress intensity factors (opening and shear modes) are computed for different load conditions and various properties of the bimaterial. The results are compared with the ones obtained in the time domain. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A continuum mechanical model for rubber-toughened polymers undergoing inelastic deformation solely by distributed crazing is introduced. Scaling relations with regard to microstructural parameters are derived analytically from a simple unit cell model. The constitutive model is calibrated from experimental data for a commercial ABS material and well captures various aspects of its deformation and failure behaviour. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Cohesive interface elements are well suited for three-dimensional crack propagation analyses as long as the crack path is known. This is the case e.g. in delamination analyses of laminated composite structures or failure analyses of adhesively bonded joints. Actually, they are widely used in such applications for both brittle and ductile systems.

As long as the strength and fracture toughness of the material are accurately captured it is generally accepted that the shape of the cohesive law has little to no influence on the mechanical behavior of the investigated structures. However, when having a look on the local behavior of different cohesive zone models, such as stress distribution in the fracture process zone, the results exhibit certain differences. These will be studied in the present contribution. Especially the local stress distribution will be investigated and the effect on the computational efficiency will be pointed out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The numerical modeling of failure mechanisms in plates and shells due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. In this paper, we extend ideas recently outlined in [1, 2] towards the phase field modeling of fracture in dimension-reduced continua with application to Kirchhoff plates and shells. The introduction of history fields, containing the maximum reference energy obtained in history, provides a very transparent representation of the coupled balance equations and allows the construction of an extremely robust operator split technique. The performance of the proposed models is demonstrated by means of representative numerical examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in dynamic problems with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. We outline a conceptual framework for phase field models of crack propagation in brittle elastic and ductile elastic-plastic solids under dynamic loading and investigate the ductile to brittle failure mode transition observed in the experiment performed by Kalthoff and Winkeler [3]. We develop incremental variational principles and consider their numerical implementations by multi-field finite element methods. To this end, we define energy storage and dissipation functions for the plastic flow including the fracture phase field. The introduction of local history fields that drive the evolution of the crack phase field inspires the construction of robust operator split schemes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Transient thermoelastic analysis of isotropic and linear thermoelastic bimaterials, which are constituted by a functionally graded (FG) layer attached to a homogeneous substrate, subjected to thermal shock is presented in this paper. For this purpose, a boundary element method for transient linear coupled thermoelasticity is developed. The material properties of the FG layer are assumed to be continuous functions of the spatial coordinates. The boundary-domain integral equations are derived by using the fundamental solutions of linear coupled thermoelasticity for the corresponding isotropic, homogeneous and linear thermoelastic solids in the Laplace-transformed domain. For the numerical solution, a collocation method with piecewise quadratic approximation is implemented. Numerical results for the dynamic stress intensity factors are presented and discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The problem of the flexibility of an infinite row of pin-loaded holes in an elastic plane or half-plane is considered within the framework of the complex potential method [1] and the theory of compound asymptotic expansions [2]. The holes are loaded by a given distribution of normal stresses with a resultant equal to the overall transmitted force. First, the relative radius of the holes is introduced as a small parameter. Then, an asymptotic expansion of the complex potentials in terms of this small parameter is constructed. This expansion is uniformly valid in the whole domain, i.e. in the vicinity of the holes as well as in the far-field. Finally, the flexibility of the row of pin-loaded holes is evaluated using this solution. In this manner, closed-form analytical approximations of the flexibility of an infinite row of pin-loaded holes in a full plane and a half-plane are obtained. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

During the past decade various new spatial discretization techniques have been developed. In particular, the usage of NURBS based shape functions, well known to the CAD community, has been adapted to finite element technology. In the present work we use the mortar finite element method for the coupling of nonconforming discretized sub-domains in the framework of nonlinear elasticity. We show that the method can be applied to isogeometric analysis with little effort, once the framework of NURBS based shape functions has been implemented. Furthermore, a specific coordinate augmentation technique allows the design of an energy-momentum scheme for the constrained mechanical system under consideration. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Explicit time integration is characterized by small time steps and efficient global operations, leading to a domination of element processing regarding CPU-time, in particular, as diagonal mass matrices are used. The Enhanced Assumed Strain (EAS) approach requires local operations in order to condense-out additional degrees of freedom. The method of Incompatible Modes (IM) is presented as an alternative, where incompatible degrees of freedom are included in the global equations, which leads to efficient element formulations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper proposes an identification method for general linear time-varying (LTV) MDOF systems (including chainlike and non-chainlike systems) based on the Hilbert-Huang Transform (HHT). First, by using Bayesian Inference and a Transitional Markov Chain Monte Carlo (TMCMC) algorithm [1], initial knowledge about the system responses and the white noise in system responses is updated based on measured system responses, which yields the posterior distributions of the noise parameters. Second, each sample system responses are obtained from the posterior distribution and are processed by HHT in order to obtain intrinsic mode functions (IMFs) and the residue as well as the corresponding analytical IMFs and the analytical residue for system responses of each DOF. Finally, the above analytical signals for each DOF are summed respectively to form new analytical responses for each set of sample system responses, which are then used in the identification equations [2] to identify the distributions of system parameters. The proposed method is applied to chainlike and non-chainlike LTV systems with three types of stiffness variations: smooth, abrupt and periodical variations. The effectiveness and accuracy of the proposed method on 1DOF and 2DOF systems is discussed in numerical simulations. System responses are perturbed by white noise, and the identified results demonstrate the robustness of the method. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present study, circular metal plates are subjected to impulsive loadings leading to geometrically and physically non-linear deformations. In the theoretical model, different structural hypotheses are implemented into a finite element code and the hypotheses leading to the most precise numerical predictions are studied. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, a coupled two-scale shell model is presented. A variational formulation and associated linearisation for the coupled global-local boundary value problem is derived. The discretisation of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretised using 8-noded or 27-noded brick elements, or solid shell elements. The coupled boundary value problem is simultaneously solved within a Newton iteration scheme. Solutions for small strain problems are computed within the so-called FE² method. In an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified. Examples show that the developed two-scale model is able to analyse the global and local mechanical behaviour of heterogeneous shell structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A new formulation of the scaled boundary finite element method (SBFEM) is presented for the analysis of circular plates in the framework of Kirchhoff's plate theory. Essential for the SBFEM is, that a domain is described by the mapping of its boundary with respect to a scaling centre. The governing partial differential equations are transformed into scaled boundary coordinates and are reduced to a set of ordinary differential equations, which can be solved in a closed-form analytical manner. If the scaling centre is selected at the root of an existent crack or notch, the SBFEM enables the effective and precise calculation of singularity orders of cracked and notched structures. The element stiffness matrices for bounded and unbounded media are derived. Numerical examples show the performance and efficiency of the method, applied to plate bending problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The focus of this work is the identification of a unit cell that is able to represent the microstructure of a closed-cell solid foam to predict the effective behaviour of the foam numerically. For the investigation, a finite element model consisting of a repeating unit cell with periodical boundary conditions is implemented. A tetrakaidecahedral foam microstructure is considered as simplified cell geometry, and a strain-energy based homogenisation concept is utilized. On the basis of image analysis imperfections are applied to the cell. The obtained model is used as a representative volume element (RVE) for further investigations of the postbuckling behaviour of the foams. Different analyses are performed and the results are compared to literature and experimental data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The main goal of the present work is to develop a structure-preserving time integrator, which is based on the works of Öttinger [2] (GENERIC formalism) and Romero [4] (Thermodynamically consistent (TC) algorithm). This intergator is called the enhanced TC algorithm for thermoviscoelastic continuums. The underlying structure is then called enhanced GENERIC, analogously to the earlier puplished thermoviscoelastic double pendulum of Krüger et al. [1]. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In brake and clutch systems kinetic energy is converted into thermal energy. Experiments show that the corresponding temperature field can develop unstable periodic structures. The temperature field couples to the displacement field by thermal expansion. Local pressure maxima in the frictional plane and the corresponding maxima in heat generated cause thermoelastic instabilities (TEI). A model describing both effects covers layers of thermoelastic materials for all necessary mechanical components of the system. The set of field equations of each layer can analytically be solved by separation of constants. These solutions must fulfill the boundary conditions e.g. in the sliding plane. A stability discussion yields whether TEI appear or not. As a study a brake system is analyzed comprising two pads pressed against a rotating disk with cooling channels inside. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel response spectrum methodology for rapid assessment of the dynamic peak acceleration response of simple railway bridges subjected to high-speed trains is presented. This methodology is based on non-dimensional characteristic bridge and train parameters, and on the shear beam theory. The effect of shear deformations should be considered, if the considered bridge is a truss structure. Depending on the train load model, response spectra are derived for each modal coordinate separately as a function of a non-dimensional speed parameter and the bridge length to wagon length ratio. An estimate of the peak response is found by statistical combination of the individual modal responses applying different rules. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A circular plate is inelastically deformed by uniform pressure, unloaded and then alternately reloaded to the same peak level. For each iteration, snap-through occurs at an increased pressure relative to the previous one, leading to additional plastic deformation. By repeating this process, the plate either fails or a limit state of deformation is reached under peak pressure without snap-through. For the case of a limit state, the results of [1] are extended to numerically determine the pressure above the peak level causing the plate to snap-through again. This is compared to the snap-through pressure of an initially unloaded spherical cap whose radius corresponds to the maximum displacement achieved in the limit case. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For electric motors light weight construction is becoming increasingly important. Therefore the mechanical behavior of the lamination stack is necessary to be known for the simulation. The stacking of a lot of sheets has a relevant influence onto the behavior of the whole motor, because of the significant contact characteristics between the sheets. Quasi-static tests are performed to identify this. In these tests an axial load, representing the packaging process, is applied onto the stacked sheets and thereafter a cyclic load is superposed. With these quasi-static tests elastic and plastic effects and a hysteretic behavior are detected. For modeling this stiffness behavior nonlinear springs and frictional elements, containing the Coulomb's law, are assembled. The nonlinearities and the hysteresis are dependent on the sheet's roughness. Moreover the behavior of the stack is influenced by the coreplate varnish viscoelasticity. With modeling these effects, the measured values can be well simulated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For the symmetrically supported Euler buckling column with both ends hinged the classical stability theory yields simple trigonometric functions as buckling modes, i.e. w(x) = A sin αx. The eigenvalues α are just multiples of π. In comparison, the analysis of the asymmetrically supported Euler buckling column with one end clamped and the other end hinged is more complicated: The buckling modes are a combination of trigonometric functions in form of w(x) = A (sin αx − αx cos (αL)). The eigenvalues follow from a transcendental equation.

Applying a geometrically exact theory to the aforementioned Euler buckling problems, a similar relation in the complexity of the analyses will naturally arise. Using, e.g., the elastica model the buckling behavior of the symmetrically supported column is represented by elliptic integrals. However, the determination of the buckling behavior of the asymmetrically supported column turns out to be much more complex and elaborate. This article presents a direct comparison of the symmetrically and asymmetrically supported buckling columns regarding their analyses by means of classical stability theory and by the geometrically exact theory of the elastica. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A method of evaluating creep response of the multipass weld based on the micro-macro mechanics approach is introduced. Multipass weld microstructure that consists from columnar, coarse and fine grained zones is considered. Materials of these constituents assumed to be isotropic. Weld metal properties of inelastic behavior have general type of symmetry and are described by the anisotropic creep constitutive model.

To model the microstructure of the multipass weld metal the representative volume element (RVE) is created for CAE Abaqus. Material properties of weld metal grain type zones are taken from the experiments. Numerical tests on uniform loading of the RVE are performed. Creep material properties for equivalent weld material are found for welds with different number of passes. The symmetry type of the creep material properties of multi-pass weld are evaluated for the equivalent weld material. As an example of macro model analysis of the welding, the creep calculation of the cylindrical shell with the welding under the uniform inner pressure is performed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Friction forces are only transferred within the the real area of contact A_real, which is usually smaller than the apparent area of contact A_o. The maximum friction stress τ_fric is therefore determined by the shear limit τ_max in the area of real contact and the fraction of the real area of contact (τ_fric = τ_max (A_real/A_o)). For rough surfaces the size of A_real is governed o by the plastic deformation of the surface roughness. We present a fully elasto-plastic halfspace contact formulation based on the work of Jacq et al. [1]. Linear elastic-plastic material behavior is modeled based on v. Mises plasticity with isotropic hardening. The algorithm gives the residual stress as well as the full plastic deformation field due to a frictionless normal contact. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The trend to extend the working ranges of flexure hinges implies large deformations during operation. To conduct a failure analysis the total deformation is decomposed into desired deformation and deviations. In particular, a flexure hinge of leaf-spring type is examined. It is modeled by the theory of elastica. The resulting boundary value problem is solved numerically for the static case by Ritz's method. It is discretized into trial functions and their free coefficients are determined from the minimum of potential energy by optimization methods. The crucial point is that the elastic energy stored in the beam is formulated intrinsically, while the potential of external conservative loads is formulated in a space-fixed coordinate system. The well-known special case of buckling of a straight cantilever beam is used for verification. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Polynomial Chaos expansion in Stochastic Finite Element Methods increases the size of the resulting linear systems dramatically. In iterative scheme which takes the underlying statistics into account is suggested for the efficient numerical solution. Additionally, an approach for the solution of von Mises stresses from the Polynomial Chaos representation of the displacement field is outlined. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work is concerned with the identification of material parameters for isotropic, incompressible hyperelastic material models. Besides the principal stretch-based strain-energy function by Ogden an invariant-based strain-energy function by Rivlin/Saunders is considered for which parameter sensitivities are derived. The identification is formulated as a least-squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements. For the finite element method low-order tetrahedral elements in a mixed displacement-pressure formulation with stabilization are considered. Special attention is payed to an adaptive mesh-refinement based on a goal-oriented a posteriori error indicator to gain reliable material parameters. To approximate error terms an element-wise recovery technique based on enhanced gradients is introduced. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The focus of this contribution is the solution of hyperelastic problems using the least-squares finite element method (LSFEM). In particular a mixed least-squares finite element formulation is provided and applied on geometrically nonlinear problems. The basis for the element formulation is a div-grad first-order system consisting of the equilibrium condition and the constitutive equation both written in a residual form. An L₂-norm is adopted on the residuals leading to a functional depending on displacements and stresses which has to be minimized. Therefore the first variations with respect to both free variables have to be zero. The solution can then be found by applying Newton's Method. For the continuous approximation of the displacements in W^1,p with p > 2, standard polynomials are used. Shape functions belonging to a Raviart-Thomas space are applied for the stress interpolation. These vector-valued functions ensure a conforming discretization of the Sobolev space H(div, Ω). Finally the proposed formulation is tested in a numerical example. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Functionally graded beams (FGBs) with an arbitrary gradation of the material properties along the thickness of the beams are analyzed. Such FGBs are of special interest in civil and mechanical engineering to improve both the thermal and the mechanical behaviour of the beams. In [1] and [3] free vibrations of functionally graded Timoshenko and Euler-Bernoulli beams have been considered. The obtained analytical solutions are based on the work of Li [2], where closed-form solutions of stress distributions, eigenfrequencies and eigenfunctions have been derived by means of a single differential equation of motion for the deflection. However, these previous works did not take into account the coupling between the longitudinal and the transverse displacements and its effects on the deformation and internal forces of the FGBs. This approach is appropriate only for a symmetrical material gradation but it may not be valid for general cases with an arbitrary material gradation.

In this paper, the coupling effects of the longitudinal and transverse displacements on the deformation and internal forces of FGBs are investigated for different beam support conditions. Analytical solutions of the corresponding boundary value problem are derived. A comparison is also made with the numerical results obtained by the finite element method (FEM). (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Subject of the investigation is a cylindrically curved thick-walled shell guided at the ends which is heated at its outer surface. In particular, the thermal conditions at the elastic limit according to Tresca's yield criterion as well as the couples occuring in the elastic and elastic-plastic state are studied. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This article analyzes the stress-state of a shear web with free edges, i.e. a rectangular plate, which is loaded by shear on two simply supported opposite edges whereas the other two opposite edges can move freely and remain unloaded. Considering the plate's plane stress-state it is obvious that at the corners the maximum equivalent stress occurs. If the plate does not buckle this stress determines its strength. However, the evaluation of the stress-state at the corners raises some difficulties. As at these points the loaded and unloaded edges meet, the development of stress concentrations is indicated. Here the fundamental question arises if these stress concentrations remain finite or if singularities occur. To analyze this question we use both, analytical and numerical considerations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A numerical approach simulating the effects of interlaminar defects on the buckling stability of layered composite struts is presented. The formulation is based on the weak form of the balance of linear momentum whilst large strains are considered. First results are presented whilst comparisons are drawn to analytically derived results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Sandwich structures made of sheets of composite materials are in widespread use, particularly in the transportation industry. Finite Element simulation of the thin, tesselated structures with complex, three-dimensional material behaviour is a challenging task for the underlying element technology. In particular, frequently used linear isoparametric approaches exhibit unphysical stiffening phenomena. Recent developments in solid-shell finite element technology aim to overcome these undesirable effects. Here, they are applied to an example of a corrugated sandwich core under transversal compression. A study of convergence is conducted with respect to commercially available shell and solid finite elements, and their ability to reproduce the bending dominated deformation state. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Thin structured sheet metals promise high potential concerning lightweight design in industrial applications regarding the classical mechanical engineering and vehicle construction as well as the aeronautics.

Compared to flat, unstructured sheet metals the component stiffness and buckling behavior can significantly be improved by structuring especially in out of plane direction.

To be able to calculate the elastic behavior of large structures from structured sheet metals a mechanical surrogate model is developed which describes effectively average material parameters based on processes of homogenization.

For the surrogate properties symmetry and antisymmetry boundaries and periodic boundaries respectively are contemplated on elementary cells whose structural mechanical behavior is decisive.

By using an energetic approach [3] the stiffnesses of large plate and shell structures can be determined by a cooperatively small amount of finite elements. By means of these material properties elastic behavior can easily be calculated. With it an efficient numerical design is guaranteed.

This explained analysis can be applied to other periodically built up plate structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytical solution of an elastic-partially plastic two-layer curved bar subjected to couples at both ends is obtained. The solution is based on Tresca's yield criterion and its associated flow rule. Numerical results for real engineering materials in partially plastic stress state are presented in graphical form. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, the numerical and experimental studies of a tall building's model with 2DOF pendulum mass damper (PMD) are considered. It is assumed that the model excitation is in the form of horizontal and/or torsional motion of the ground caused by earthquake.

The construction consists of the main system (tall building's model) and a double pendulum mass damper, which is attuned to the first (bending) and the second (torsional) eigenfrequencies of the main structure. The analysis focuses on reduction of structure vibration caused by horizontal or torsional component of ground motions. Therefore, results presented in this work show efficiency of 2DOF PMD for vibration reduction.

The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model-scale building with 2DOF PMD. Model consists of twenty five recurrent storeys (height 2.5m) with a PMD located on the highest one. Shaking table device is used to simulate an earthquake excitation in horizontal and torsional component, independently. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The approach of Sensitivity Analysis with Green's Functions (SAGF) [1,2] was developed to predict changes in deformations, stresses or eigenfrequencies of structures resulting from stiffness modifications or cracking by considering only the weakened or damaged parts of the structures. This approach results in a local analysis instead of a global analysis by recalculating the whole structure. Consequently, it is computationally less time-consuming than the conventional methods based on a global analysis. The key idea of the SAGF approach is based on the comparison between the elastic strain energies of the original and the weakened structures and the substitution of the virtual displacements by the corresponding Green's functions [1, 2].

Furthermore, an approximate approach for the sensitivity analysis was suggested which is described in [1, 3] in details. This approach enables us to predict the changes in the structural responses due to the stiffness weakening in the beam or in the elastic Winkler foundation by considering only the internal forces or the deflections of the original unweakened system. In addition, an iterative method was developed to enhance the accuracy of the SAGF approach.

In this paper, the local SAGF method for sensitivity analysis of elastic beams on Winker foundation with stiffness weakening is presented. The accuracy and the efficiency of the proposed method are verified by using a numerical example. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An approach for the simulation of the elastic material responses using stochastic generation of material samples and a subdomain-based FEM simulation is presented. Both the single-grain geometries and the lattice orientations are stochastically simulated. This simulations can be used to build a Material Library of responses which must be computed only once for a given material. Furthermore, the Library can be used in a fast two-scale simulation avoiding any detailed computation in the microscale. In this contribution, the basic ideas of the computational algorithm are presented and some results of the material library for Steel DC01 are given. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For high-power low-flow operating conditions associated with unfavorable power distribution Boiling Water Reactor (BWR) operation requires maintaining a certain distance to the stability limit given. The stability boundary with respect to small perturbations is given by analytical methods. Supplementary evaluation of non-linear states require time-consuming numerical integration or experimental data and strongly depend on the considered transient. Developing a self-contained methodology for investigating the full non-linear BWR system parameter space at low computational cost supplements established methods. The methodology of Reduced Order Modeling based on Proper Orthogonal Decomposition (ROM-POD) is tested for this purpose and validation in terms of the Korteweg de-Vries (KdV) equation. A transient analysis of simplified reactor physics [1] yields a low-rank ROM and is depending on the chosen transients but not on the details. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Grinding is a very complex and high dynamical material removal process with stochastically distributed grain engagements and strong varying local contact conditions. Over a long time only macroscopic effects are analyzed and predicted by empirical relations. To understand the dynamical behavior also local effects must be considered.

Therefore, the local contact conditions and especially the time-dependent friction coefficient are analyzed. One detected effect is the dependency of the friction coefficient on the normal forces and on their time history, so a hysteresis loop occurs for increasing and decreasing values. With the force dependent friction coefficient local and dynamic effects are physically interpretable. In contrast, the global mean friction coefficient is constant over the entire force range which describes only quasi-stationary effects. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The goal of this contribution is to calculate the the friction coefficient for a scanned surface of a worn brake pad. The data shows that the asperities can be approximated by paraboloids which allows to calculate the contact force and area with the Hertz contact model if the deformation is elastic. The friction force is calculated with the Bowden-Tabor approach which suggests that the friction force is the force to shear apart contacting asperities. This is considered to be the dominant friction cause in dry contact. To generate many surfaces with similar peak statistics the spectral decomposition is used. The friction coefficient and it's stochastic properties is calculated for these surfaces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Stochastic processes are a common way of describing systems that are subjected to random influences. Technical systems may be excited by road roughness or wind gusts, for example, as well as fluctuating system parameters, which can all be described by stochastic differential equations. In previous works by the author and others (see [1], for example) it has been demonstrated how a Galerkin-method can be used to obtain global numerical solutions of the Fokker-Planck-Equation (FPE) for nonlinear random systems. Computational efforts are reduced by orthogonal polynomial expansion of approximate solutions so that probability density functions (pdfs) for comparably high-dimensional problems have been computed successfully. Stationary mechanical systems with dimensions up to d = 10 have been investigated, including polynomial as well as non-smooth nonlinearities. This article presents results for different energy-harvester-systems under stochastic excitation, a field of research that has become the subject of increasing attention in the last years. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The interaction between a flexible structure and flowing fluid can cause flow-induced vibrations and the steady state may loose stability by divergence or flutter, thus leading to undesirable dynamic behaviour.

As a model for fluid-structure-interaction a planar channel guiding a flowing fluid is studied. It can be shown that for thin channels the coupling effects are strong [1] and therefore the focus of this contribution is to investigate the behaviour of a channel, where the structural displacements are non-negligible compared to the gap width. Due to this comparatively large amplitudes a linear description of the interface between fluid and structure will not be sufficient anymore and the relation between the Eulerian description of the fluid and the Lagrangian description of the structure must be taken into account: eventually, this yields nonlinear boundary conditions. Furthermore in narrow gaps the viscosity of the fluid cannot be ignored [2]. Hence the effect of viscosity will also be considered within this contribution. In order to allow for analytical results and keep the focus on the effects due to the moving interface, the fluid flow is modelled using lubrication theory. The linear stability of the steady state ist investigated as well as the influence of the inherent nonlinearities of the coupled problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Es wird ein mechanisches Modell zur Beschreibung des bewegten Sägedrahtes unter Einwirkung des Siliziumblocks (Ingot) vorgestellt. Mit dem Prinzip von HAMILTON wird, unter der Voraussetzung nichtlinearer Verformungskinematik sowie unter Berücksichtigung der Dehn- und Biegesteifigkeit des Drahtes, das Variationsproblem und die Bewegungsgleichungen hergeleitet. Die Wirkung des Ingot auf den bewegten Draht wird als Folgelast modelliert. Ausgehend vom Variationsproblem wird mit einem gemischten RITZ-Ansatz die stationäre Lage des Drahtes für verschiedene Einflussparameter berechnet und Stabilitätsuntersuchungen durchgeführt. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim in high-performance sports activities is reaching the optimum between high efficiency and low risk of injuries during workout. This paper wants to investigate several types of human motion in interaction with a compliant ground. The influence of the surface parameters on the human metabolic cost consumption and the reaction force is analysed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A many-degrees-of-freedom model of rotor stator contact is presented. The stability analysis of the synchronous motion of the simple JEFFCOTT rotor contacting a single-mass stator is extended to systems with many degrees of freedom. The stationary synchronous motion as well as its stability are validated by direct numerical integration of the differential equations. The resulting dynamics is exemplified in two examples, which may be quite different than the dynamics of the simple JEFFCOTT rotor. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental determination of frequency response function of nonlinear systems is difficult when there exists more than one solution branch. Depending on the system at hand, various types of jump phenomena can be observed and in the example of the well-known Duffing-oscillator, it is not possible to experimentally determine the unstable solution branch if the system is excited by a harmonic force. In the present paper we investigate the Duffing-oscillator and present a method, which allows to reformulate the equation of motion of the system with force-excitation in the form of an equivalent self-excited system. Considering the phase between force and response as the input variable, it is possible to evaluate the frequency of the systems vibration for any given phase shift. In the same way the corresponding response amplitude is determined. An experimental set-up is presented, which is used to validate the performance of the method. Measurements of the backbone curve are performed and discussed on the background of theoretical predictions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We investigate the influence of viscous damping on the shape and stability of travelling waves induced by Coulomb friction between a rotating rigid shaft and an annular elastic cylinder. As expected, the damping causes the travelling wave solutions to become smoother and more stable. It also decreases the amplitude and range of separation solutions and may destroy the travelling waves by grazing bifurcations at large values of the damping parameters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The two-dimensional non-linear dynamics of a liquid-filled tube is considered. The tube is clamped at the upper end, a point mass is fixed to its free lower end and laterally it is supported by two springs. The uniform flow velocity of the fluid, the end mass, the spring constant and the vertical position of the springs are considered as the distinguished parameters of the problem. A linear stability analysis shows that the (degenerate) case of a Takens-Bogdanov-Hopf bifurcation exists, which is associated with a high frequency flutter movement superimposed on a low frequency flutter around a statically buckled state of the tube. We account for this degenerate case by indicating the parameter regime necessary for its occurence and and give the bifurcation diagram for the trivial equilibrium position of the tube. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

To capture the complex elastoplastic response of many materials, classical isotropic and kinematic hardening alone are often not sufficient. Typical phenomena which cannot be predicted by the aforementioned hardening models include, among others, cross hardening or more generally, the distortion of the yield function. However, such phenomena do play an important role in several applications in particular, for non-radial loading paths. Thus, they usually cannot be ignored. In the present contribution, a novel macroscopic model capturing all such effects is proposed. In contrast to most of the existing models in the literature, it is strictly derived from thermodynamical arguments. Furthermore, it is the first macroscopic model including distortional hardening which is also variationally consistent. More explicitly, all state variables follow naturally from energy minimization within advocated framework. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The martensitic transformation is described using a phase field model which is in mathematical terms the regularization of a sharp interface approach. In this work, up to two martensitic orientation variants are considered. The evolution of microstructure is assumed to follow a time dependent Ginzburg-Landau equation. The coupled problem of the mechanical balance equation and the evolution equations is solved using finite elements and an implicit time integration scheme. In this work, the global energy evolution during the martensitic transformation and the influence of external loads on the formation of the different martensitic phases are studied in 2d. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution focuses on two different developments of mechanical-computational methods for the optimal determination of the initial shape of formed functional components knowing the deformed configuration, the applied loads and the boundary conditions. The first method uses an inverse mechanical formulation and can be applied to materials with hyperelastic behaviors. For materials with elastoplastic properties this method is not advocated, without knowing the final plastic strains, due to the non uniqueness of the solution. The second method uses a shape optimization formulation in the sense of an inverse problem via successive iterations of the direct problem. For hyperelastic materials the inverse mechanical formulation is preferred for its velocity and the non exhibition of possible mesh distortions. In the shape optimization formulation mesh distortions can be avoided by an update of the reference configuration of the functional part. Both methods are using a formulation in the logarithmic strain space. A numerical example for materials with isotropic elastoplastic behaviors illustrates the shape optimization formulation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We develop a nonlinear incompressible multiphase material model in a Cosserat continuum with microstructure. The free energy of the material is enriched with an interaction potential taking into account the intergranular kinematics at the continuum scale. As a result the total energy becomes non-convex, thus giving rise to the development of microstructural phases. To guarantee the existence of minimizers an exact quasi-convex envelope of the corresponding energy functional is derived. As a result a three phase material energy appears, among them two of the phases are with microstructure in the translational motion (displacment field) and micromotion (microrotation field), whereas the third phase is without internal structure. The corresponding relaxed energy is then used for finding the minimizers of the two field minimization problem corresponding to a Cosserat continuum. Results from a numerical example predicting the development of microstructure in the material are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution, the previously proposed network evolution model [1] for carbon black filled elastomers is further studied. First, we show that the model does not contradict the second law of thermodynamics and is thus thermodynamically consistent. On the basis of new experimental data the influence of filler concentration on the material parameters is further examined. Accordingly, this influence concerns only three material parameters and is approximated by phenomenological relations. These relations enable one to simulate rubbers based on the same compound with various filler concentrations. Finally, the model is implemented into the FE-Software ABAQUS and illustrated by a number of numerical examples. The examples demonstrate good agreement with experimental results with respect to the Mullins-Effect, permanent set and induced anisotropy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Colloidal structures inside solutions are usually considered as rigid bodies or linear springs. However, recent experimental results show a strongly nonlinear mechanical response of large clusters. In this contribution, the nonlinear elastic behavior of the colloidal structures inside polymeric solutions is studied. So far, the influences of initial length and fractal dimension on the elastic response of colloidal structures have mostly been considered by scaling theory. Here, we additionally take into account a deformation induced evolution of the aggregate structure which is mainly influenced by inter-particle interactions. To this end, central and lateral (non-central) inter-particle forces are considered separately. Next, the directional stiffness of the colloidal structure is evaluated by using the concept of a backbone chain. The backbone chain is a unique path between two ends of the colloidal structure that carries the main portion of load. The mechanical response of the backbone chain depends on aggregate geometry, deformation history and moreover, on the nature and the strength of the inter-particle interactions. The aggregate geometry is described by means of the angular averaging concept. The so-obtained model can further be generalized for all types of colloidal structures with central and lateral inter-particle forces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Lower-bound limit and shakedown analysis of periodic composites with the consideration of kinematic hardening are carried out on the representative volume element level. In combination with homogenization theory, the homogenized macroscopic admissible loading domains are determined. Furthermore, the strengths of periodic composites by using elastic perfectly plastic, unlimited and linear limited kinematic hardening material models are calculated and compared. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Heat treatment is an important part of the manufacturing of metallic products, especially in powder coating processes. It provides an efficient way to improve the properties of the metal as e.g. hardness by controlling the rate of diffusion and the rate of cooling within the microstructure. The process-integrated powder coating by radial axial rolling of rings is a new hybrid production technique which is introduced in [1]. The applied temperatures in hot rolling are within the range of austenitizing temperatures for the investigated steels [2]. Therefore, reasonably controlling the temperature is an important task [3]. The paper is concerned with the integration of heat treatment of the rolled ring into the subsequent cooling process. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation.

Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present a novel approach for the simulation of solid to solid phase-transformations in polycrystalline materials. To facilitate the utilization of a non-affine micro-sphere formulation with volumetric-deviatoric split, we introduce Helmholtz free energy functions depending on volumetric and deviatoric strain measures for the underlying scalar-valued phase-transformation model. As an extension of affine micro-sphere models [5], the non-affine micro-sphere formulation with volumetric-deviatoric split allows to capture different Young's moduli and Poisson's ratios on the macro-scale [1]. As a consequence, the temperature-dependent free energy assigned to each individual phase takes the form of an elliptic paraboloid in volumetric-deviatoric strain space, where the energy landscape of the overall material is obtained from the contributions of the individual constituents. For the evolution of volume fractions, we use an approach based on statistical physics–taking into account actual Gibbs energy barriers and transformation probabilities [2]. The computation of individual energy barriers between the phases considered is enabled by numerical minimization of parametric intersection curves of elliptic Gibbs energy paraboloids. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper the full coupled quasi-static theory of poroelasticity for materials with double porosity is considered. The basic boundary value problems (BVPs) of the steady vibrations are investigated. The uniqueness theorems of the internal BVPs of steady vibrations are proved. The basic properties of elastopotentials are established. The existence of regular solutions of the BVPs by means of the boundary integral equations method and the theory of singular integral equations is proved. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper the linear theory of viscoelasticity for Kelvin-Voigt materials with voids is considered. The uniqueness and existence theorems for internal boundary value problem (BVP) of steady vibrations are proved by means of the potential method (boundary integral method) and the theory of singular integral equations. The application of this method to the 3D BVP of the considered theory reduces this problem to 2D singular integral equation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Common structural optimisation problems consist of problem-specific objective functions which have to be minimised mathematically with respect to design and state variables taking into account particular constraints. In contrast to this, we adopt a conceptually different approach for the design of a structure which is not based on a topology-optimisation technique. Instead, we apply a one-dimensional energy-driven constitutive evolution equation for the referential density–originally proposed for the simulation of remodelling effects in bones–and embed this into the micro-sphere-concept to end up with a three-dimensional anisotropic growth formulation. The objective of this contribution is to investigate this approach with emphasis on its application to structural design problems by means of two three-dimensional benchmark-type boundary value problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale.

Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting load-displacement-behaviour as well as the specific heat generation due to friction and plastic dissipation.

A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work, an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In automotive industry research is done to replace high strength steel by combinations of steel and carbon-fibre prepregs (pre-impregnated fibres). It is planned to form both steel and uncured prepregs in one step followed by the curing process under pressure in the forming die. The ability to simulate the mechanical behaviour during forming and curing would allow more economical processes. The simulation of prepregs must regard highly anisotropic, viscoelastic and thermal- chemical properties. For this the model is split into an anisotropic elastic part, which represents the fibre fraction and an isotropic, viscoelastic part, representing the matrix. This part also contains curing, causing a dependency on time and temperature. During deep-drawing large deformations are occurring, so a large strain model regarding anisotropy, viscoelasticity and curing has been developed. Also experiments were made to validate this model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Viscoelastic materials show a significant frequency and predeformation dependent behaviour under loadings consisting of large predeformations superimposed by small harmonic deformations. Based on further material models of Haupt & Lion [1] and Lion, Retka & Rendek [2] we introduce a recently developed constitutive approach of finite viscoelasticity in the frequency domain that is able to describe the frequency and predeformation dependent material behaviour with respect to storage and loss modulus. The constitutive equations are geometrically linearised in the neighbourhood of the predeformation and will be evaluated in the frequency domain. Furthermore a formulation for incompressible material behaviour is introduced and the corresponding dynamic modulus tensors are derived. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The nanoindentation technique is established in the field of material characterization at small dimensions. It is daily practice to analyze nanoindentation data with an almost “classical” formula based on the publications by Oliver and Pharr and Fischer-Cripps. The procedure works well for elastic-time independent plastic material behavior, for example copper and the calibration material fused silica, even at higher test temperatures. However, low melting solder materials are susceptible to creep behavior. For this reason, additional analysis procedures are required to determine the material parameters more precisely. In this paper the authors want to give an introduction to an “enhanced” analysis of nanoindentation data based on rheological models, which are often used to describe the time-dependence of material response. Two examples of such models are the MAXWELL- and the KELVIN-body. The authors present a rheological model, published by Mencik in 2011 [1], in context with the corresponding equation which is used to extract the material properties from the recorded data. Results of the analysis at the calibration material fused silica are presented and discussed together with the material parameters published in the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution a new constitutive model for transversely isotropic materials is presented. The proposed model is based on the multiplicative decomposition of the deformation gradient into one part containing the deformation only in the direction of anisotropy and another part describing the remaining deformation. This clear assignment leads to a decoupling of the stress-state. The model is investigated analytically in view of simple tension. Moreover, an inhomogenous deformation is solved using a finite elements simulation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present paper, the surface roughness effects in nanoindentation of soft polymers are modelled numerically based on the approach utilising the phenomenological concepts. A real surface topography is characterised by using multi-level of protuberance-on-protuberance profiles. Following the real surface topography is simplified by one-level or multi-level sine curve profiles. Finally, the surface roughness effects are quantified related to the force-displacement data as well as to the identified material parameters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastomers are widely used in today's life. The material is characterized by large deformability upon failure, elastic and time dependent as well as non-time dependent effects which can be also a function of temperature. In addition, cyclically loaded components show heat build-up which is due to dissipation. As a result, the temperature evolution of an elastomeric component can strongly influence the material properties and durability characteristics. Representing best the real thermo-mechanical behaviour of an elastomeric component in its design process is one motivation for the use of sophisticated, coupled material approaches within numerical simulations. In order to assess the durability characteristics, for example regarding crack propagation, material forces (configurational forces) are one possible approach to be applied. In the present contribution, the implementation of material forces for a thermo-mechanically coupled material model including a continuum mechanical damage (CMD) approach is demonstrated in the context of the Finite Element Method (FEM). Special emphasis is given to material forces resulting from internal variables (viscosity and damage variables), temperature field evolution and dynamic loading. Using the example of an elastomeric component, for which the material model parameters have been previously identified by a uniaxial extension test, material forces are evaluated quantitatively. The influence of each contribution (internal variables, temperature field and dynamics) is illustrated and compared to the overall material force response. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In dieser Arbeit werden zunächst für eine handelsübliche AFM-Paste die Parameter eines nicht-Newtonschen Stoffgesetzes experimentell in Rotationsrheometerversuchen bestimmt und die Ergebnisse an einer weiteren Versuchsreihe (Düsenauspressversuche) mit Hilfr einer FEM-Simulation überprüft. Danach werden ein einfaches Abtragsmodell vorgestellt und die Funktionsfähigkeit dieses Modells an einem Beispiel demonstriert. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Within this contribution, the focus is placed on the simulation of the isochoric behavior of polymers during the curing process. To this end, a model based on the assumption of free energy in the form of a convolution integral is applied. Since this allows the implementation of the time-dependent material parameters, the free energy is interpreted as the total accumulated energy. Different from this, the strain energy is related to the current state of deformation and used to define the temporary stiffness. In order to avoid volume locking effects typical of isochoric materials, the free energy is furthermore split into a volumetric and a deviatoric part. A multifield description depending on the displacements, volume change and hydrostatic pressure is introduced as well. The model is implemented within a single- and multiscale FE program and used to simulate the behavior of homogeneous and microheterogeneous polymers. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Material microstructures in finite single-slip crystal plasticity occur and evolve due to deformation. Their formation is not arbitrary, they tend to form structured spatial patterns. This hints at a universal underlying process. As in the approach of D. Kochmann and K. Hackl, we use a variational framework, focusing on the Lagrange functional to describe the evolving mircrostructure. We modify this approach by introducing a small smooth transition zone between the domains in order to improve the numerical treatment. We present explicit time-evolution equations for the volume fractions and the internal variables. We outline a numerical scheme. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The structure of complicated phenomenological material models at finite strains is often exemplified with the help of rheological elements. Thereby, simple material behaviour, i.e. elasticity or viscous and plastic flow, are composes by components. In our approach, we directly apply this concept to obtain material models at finite strains. Towards this end, the thermodynamically consistent material behaviour of single elements is defined first. Subsequently, the elements are connected by evaluation of stress equilibria equations formulated on interconnecting configurations. The basic equations of this concept are presented using the example of nonlinear viscoelasticity of Maxwell type. The model results from a series connection of an elastic and a viscous element, whereas both are formulated in a thermodynamically consistent way within the framework on nonlinear continuum mechanics. Furthermore, an approach of numerical implementation using the stress equilibria is suggested. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A phenomenological model of metal viscoplasticity, which takes combined isotropic, kinematic, and distortional hardening into account, is motivated by a new rheological model. The distinctive advantage of the material model is that any smooth convex saturated form of the yield surface which is symmetric with respect to the recent loading direction can be captured. In particular, an arbitrary sharpening of the saturated yield locus in the loading direction combined with a flattening on the opposite side can be covered. Moreover, the yield locus evolves smoothly and its convexity is guaranteed at each hardening stage. The underlying two-dimensional rheological analogy can be used to provide insight into the main constitutive assumptions. This rheological model is utilized as a guideline for the construction of phenomenological constitutive relations. The distortion of the yield surface is described with the help of a so-called distortional backstress. Thus, 2nd rank tensors are utilized only. The resulting material model is thermodynamically consistent. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The microscale morphology of micro machined component surfaces is directly connected to the heterogeneous microstructure. The deformation depends on the crystal structure, in case of the considered cp-titanium, the hcp crystal structure. In a first approach the crystal plastic deformation is modeled with isotropic hardening. A visco-plastic evolution law accounts for the rate dependency. The concept of configurational forces is used with the framework of crystal plasticity to model the cutting process of cp-titanium. The setting is implemented into the finite element method. The examples show the effect of the material heterogeneity on the deforamtion behavior and on the related configurational forces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Within the framework of finite elements the linearization within a Newton-like method requires the computation of the so-called consistent tangent operator. There are several possibilities to get these derivatives. Three methods, namely analytical, numerical and automatic differentiation, for tangent generation will be analyzed concerning the simulation time and applicability for three different constitutive models. These models are a finite strain hyperelasticity model, finite strain viscoplasticity model for metal powders and a small strain thermoviscoplasticity model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Material parameter identification is the necessary link between constitutive modeling and application of material models in complex simulations of real world problems. We present an approach to make use of already developed stress algorithms for three-dimensional finite-element computations in terms of a reduction to uniaxial tensile tests for material parameter identification. Strain-driven stress algorithms lead to the approach of solving differential-algebraic equations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work deals with the generation of artificial data based on experimental data for adhesive materials and the application of this data to the inverse and the direct problem. In reality there are only a very limited number of experimental data available. Therefore, the prediction of material behaviour is difficult and a statistical analysis with a stochastic proved thesis is nearly impossible. In order to increase the number of tests a method of stochastic simulation based on time series analysis is applied.

With artificial data an arbitrary number of data is available and the process of the parameter identification can be statistically analysed. Additionally, one example is shown, which adapts the analysed material parameter to the direct problem. The stochastic finite element method is used to take into account the distribution and deviation of the fracture strain. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work we develop a model to describe the induced plasticity of polymers at large deformations. Polymers such as stretch films exhibit a pronounced strength in the loading direction. The undeformed state of the films is isotropic, whereas after the uni-axial loading the material becomes anisotropic. In order to consider this induced anisotropy during the stretch process, a spectral decomposition of the inelastic right CAUCHY-GREEN tensor is done. Therefore, the yield function can be formulated as a function of the anisotropic tensor, where again the anisotropic tensor is a function of the maximum eigenvalue. A backward EULER scheme is used for updating the evolution equations, and the algorithmic tangent operator is derived. The numerical implementation of the resulting set of constitutive equations is used in a finite element program and for parameter identification. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Within the last years the goal of industrial manufacturing processes – such as tube forming – has shifted towards an optimization of technological as well as mechanical properties of the manufactured structures. For example, during the forming procedure of sheets made of austenitic stainless steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to achieve optimal structural properties of the manufactured tube with respect to very high-cycle fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained [1].

On the basis of experimental investigations this contribution deals with the numerical simulation of the tube-forming process with special consideration of the martensite ratio c as a function of temperature and deformation field. For this purpose we extend an existing martensite model on polyaxial states of stress and compare experimental results and numerical simulations for the modified model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In a material space-time manifold an expression for the entropy production is developed. It is based on a Lagrangian formulation for a hyperelastic solid. The material structure and heat transfer are represented by a tetrad field. The derivatives of the Lagrangian with respect to the time-like vector of the tetrad yields entropy density and current. An identity for the divergence of this four-current follows from the invariance of the Lagrangian and yields the entropy production due to heat transfer and defect movement. The latter part only depends on a kind of deviatoric stress if the conservation of mass is considered. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A new ideal body is proposed for representing isotropic hardening. Hence, a rheological model of thermoviscoplasticity may be assembled with linear isotropic and kinematic hardening and nonlinear strain rate sensitivity. The related constitutive equations including the yield function and the flow rule are directly deduced from the kinematics and the stress equilibrium of the rheological network and result in a well-known model. Based on the free energy of the rheological network, the equation of heat conduction is obtained with the dissipative heat source term, driven by plastic deformations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Fibre reinforced composites consisting of several layers, each of which is composed of a woven fabric embedded in a matrix material, are investigated in this paper. Such materials are characterized by a complex anisotropic behavior, which necessitates a fully three-dimensional formulation of the constitutive equations. On the other hand, they are frequently used in thin shell-like applications. In order to account for the three-dimensional material law while still providing the suitable shape for thin structures, a solid-shell finite element for fibre composite materials is presented herein. Locking phenomena are treated by both the enhanced assumed strain (EAS) concept and the assumed natural strain concept (ANS). Using reduced integration together with hourglass stabilization leads to high computational efficiency. The anisotropic constitutive behavior of the composites is reflected by a micromechanically motivated continuum model, which –together with the solid-shell formulation– allows for an accurate representation of the through-the-thickness stress distribution even for thin structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present work, we propose a model for shape memory polymers based on the idea of the multiplicative decomposition of the deformation gradient. Evolution equations for the several deformation components are presented that provide for the storage of the entropy-elastic strain and its recovery during the transition between the frozen phase and the active phase. First characteristic shape memory cycles for small and large deformations will be shown as a last point. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper will give a short overview about a multi-scale modelling approach for bituminous asphalt concrete. The goal is to describe the micro-heterogeneous medium by a homogeneous surrogate medium, which has similar effective mechanical properties. Starting from the varying constitutive behaviour on the micro-scale, our up-scaling procedure is realised via volume averaging techniques. By use of a Finite-Element model, the results for different types of boundary conditions (BCs) and their influence on the properties of the compund are investigated on the effective scale. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper is concerned with the broad class of Liner Thermoelastic (LTE) models for Shape Memory Polymers (SMPs) which unifies numerous constitutive theories proposed in the literature for this kind of smart material. It is shown that the response functions for the general model of this class may be determined directly from experimental data measured in standard thermomechanical cyclic tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Over the past decades, several constitutive models accounting for finite viscoplasticity and failure in glassy polymers were developed. However, depending on thermal and loading rate conditions, the response might change from ductile to brittle. This brittle response is characterized by inelastically deformed zones, so-called crazes, having the thickness of micrometers and spanning at some fractions of a millimeter, containing a dense array of fibrils interspersed with elongated voids, detailed discussion e.g. [1]. The shear yielding and crazing are not completely independent excluding each other. Present models introduce crazing either discrete by cohesive surfaces, e.g. [2], or continuous, see [3]. In this work, we outline an extension of a ductile plasticity model towards (i) the description of volumetric directional plasticity effect due to crazing and (ii) the modeling of the local failure due to fracture. The ultimate amount of volumetric plastic craze strain is bounded by a limiting value, where failure occurs. In a second step, the modeling of subsequent failure mechanisms is realized by introducing a fracture phase field, characterizing via an auxiliary variable the crack. Here, we adopt structures of a continuum phase field model of fracture in brittle solids [4], and modify it for a fracture driving term related to the volumetric plastic deformation of the crazes. We demonstrate the performance of proposed formulation by means of a representative boundary value problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work deals with modeling the mechanical behavior of thermoplastic polymers in the finite strain regime over a wide range of temperatures. Thereby, special emphasis is put on the incorporation of an initial anisotropy in terms of “frozen-in” molecular orientation which results from a preceding manufacturing process. A computational example is discussed which considers an injection molded plate undergoing inhomogeneous deformation (buckling) during re-heating. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We develop a micromechanical material model for phase transformation from austenite to bainite for a polycrystalline low alloys steel. In this material (e.g. 51CrV4) the phase changes from austenite to perlite-ferrite, bainite or martensite, respectively. This work is concerned with phase transformation between austenite and n-bainite variants in differently orientated grains. The characteristic features of bainite formation are the combination of time-dependent transformation kinetics and lattice shearing in the microstructure. These effects are considered on the microscale and transferred to the polycrystalline macroscale by means of homogenisation of stochastically orientated grains. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

With the ongoing trend of miniaturization and nanotechnology, the predictive modeling of size effects plays an increasingly important role in metal plasticity. The description of such size effects requires gradient-extended theories of crystal plasticity. We outline a new viscous regularized formulation of rate-independent gradient crystal plasticity for full multislip scenarios. To this end, we exploit in a systematic manner the long- and short-range nature of the involved variables. It is shown that the evolution of the short-range state is fully determined by the evolution of the long-range state. This separation into long- and short-range states is systematically exploited in the algorithmic treatment by a new update structure, where the short-range variables play the role of a local history base. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In line with our formerly presented continuum micromechanical model [4,5] of the laminate microstructure of martensite, we here modify and reformulate the model to further its simplicity and clarity. The basic postulates are slightly altered. However, the approach remains the same, namely the kinematic assumption of nearly-planar laminate geometry put into an energy minimization framework with proper ansatzes of twin-interface and boundary energies. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Some rheological materials, such as melting polymers, cosmetic creams, ketchup, toothpaste, can be modeled as non-NEWTONian fluids by using a non-linear constitutive relation. An incompressible flow of this kind of amorphous matter can be considered as a thermodynamic process, and a solution for the pressure, velocity and temperature fields describe it fully. Since such flow processes are generally irreversible, entropy is produced leading to dissipation in the system. This energy loss can be measured indirectly in a cone/plate viscometer which is used to determine viscosity of a BINGHAM fluid. While dissipation is an observable quantity we also want to be able to calculate it. Thus the goal of this work is to explain briefly how to compute a transient flow of a viscous fluid in two-dimensional channel under a sinusoidal traction and calculate the dissipated energy for non-NEWTONian fluids. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Rubber-like materials can deform largely and non-linearly upon loading and return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behaviour of such randomly-oriented micro-structure, several phenomenological and micro-mechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e. uniaxial tension, equibiaxial tension and pure shear have been derived and the performances of the models are analysed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Microwave heating is becoming of growing importance in material sciences in the last two decades. Due to the volumetric heating effect, microwave heating offers an energy efficient way of processing materials in several ways. The modeling and simulation of material processing with microwaves with respect to the material structure is a challenging task. The corresponding mathematical modeling results in a coupled, multiscale problem in space and time consisting of Maxwell equations, the heat equation and a temperature-dependent description of the dielectric properties of them material under investigation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Kohn-Sham equations resemble a nonlinear eigenvalue problem for the determination of the electronic structure of an atomic system, where the electrons are exposed to an effective potential, accounting for the Coulomb and quantum mechanical interactions between the particles. The effectiveness of the potential requires an iterative solution procedure, until self-consistency is reached. This work illustrates the implementation of the self consistent field algorithm based on nested finite elements spaces and analyzes its properties in the case of all-electron calculations on atoms as large as the noble gas Xenon. All-electron calculations have maximal requirements onto the numerical basis, as it must be able to represent all the orthogonal electronic wavefunctions simultaneously together with the electrostatic potential, showing singularities at the positions of the atoms. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

As potential material for artificial muscles and haptic displays, dielectric elastomer provides large deformations with lower cost and high efficiency. The material behaves nonlinearly in both the kinematics and the constitutive relation. In this work, the nonlinear equation of motion for a dielectric elastomer actuator with a sandwich structure under constant electric potential is derived from the energy conservation condition. The equation of motion is numerically solved, and the results are discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this article, a macroscopic 4-phase model, based on the Theory of Porous Media, is presented to simulate healing processes in a polymere matrix. The healing process is described by the phase transition of two constituents, i.e., from liquid like healing agents to solid like healed material. As a first step, the healing mechanism begins at a certain time and is not driven by a healing criterion. A numerical example will be presented to demonstrate the applicability of the model in view of the description of healing processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A coupled partial differential equation (PDE) system, stemming from the mathematical modelling of a coupled phenomenon, is usually solved numerically following a monolithic or a decoupled solution method. In spite of the potential unconditional stability offered by monolithic solvers, their usage for solving complex problems sometimes proves cumbersome. This has motivated the development of various partitioned and staggered solution strategies, generally known as decoupled solution schemes. To this end, the problem is broken down into several isolated yet communicating sub-problems that are independently advanced in time, possibly by different integrators. Nevertheless, using a decoupled solver introduces additional errors to the system and, therefore, may jeopardise the stability of the solution [1]. Consequently, to scrutinise the stability of the solution scheme becomes a pertinent step in proposing decoupled solution strategies. Here, we endeavour to present a practical stability analysis algorithm, which can readily be used to reveal the stability condition of numerical solvers. To illustrate its capabilities, the algorithm is then utilised for the stability analysis of solution schemes applied to multi variate coupled PDE systems resulting from the mathematical modelling of surface- and volume-coupled multi-field problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present work we study toughness variation of ferroelectric materials (PZT-5H) considering different scales for different poling and loading conditions. On the macro-scale we apply an extended theory of stresses at interfaces in dielectric solids. Further, on the micro-scale, nonlinear effects are introduced by applying the small scale switching approximation. The analysis is done considering the full anisotropy and electromechanical coupling of the material. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A common way of solving multi-physics problems is the use of a partitioned approach. To this end specialized solvers are utilized for the different subproblems and linked via a common communication interface. In this paper a communication interface is presented, which is capable of dealing with different kind of coupled problems. The subproblems may be discretized separately and linked either through a common boundary or by a common volume region.

In order to stabilize and to accelerate the implicit coupling iteration different relaxation techniques and predictor methods are implemented. Finally, the coupling interface is applied to a well-known fluid-structure interaction (FSI) benchmark. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution, a macroscopic quadruple model for the simulation of freezing and thawing processes in fluid filled porous media is presented. The main focus lies on the description of the distribution of fluid and ice pressure as well as solid deformation before, during and after the ice formation in consideration of energetic and capillary effects. Furthermore, the porosity change of the porous material is considered, i.e., the variation of permeability during ice formation will be simulated. The illustrated results of numerical examples will be presented to demonstrate the practical application of the model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A partitioned coupling scheme for problems of thermo-elasticity at finite strains is presented. The coupling between the mechanical and thermal field is one of the most important multi-physics problem. Typically two different strategies are used to find an accurate solution for both fields: Partitioned or staggered coupling schemes, in which the mechanics and heat transfer is treated as a single field problem, or a monolithic solution of the full problem. Monolithic formulations have the drawback of a non-symmetric system which may lead to extremely large computational costs. Because partitioned schemes avoid this problem and allow for numerical formulations which are more flexible, we consider a staggered coupling algorithm which decouples the mechanical and the thermal field into partitioned symmetric sub-problems by means of an isothermal operator-split. In order to stabilize and to accelerate the convergence of the partitioned scheme, two different methods are employed: dynamic relaxation and a reduced order model quasi-Newton method. A numerical simulation of a quasi-static problem is presented investigating the performance of accelerated coupling schemes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Ultrasonic wire bonding is a method applied in electronic packaging to fabricate interconnections between two devices at ambient temperature. In order to investigate the material diffusion during this process, the occurring thermal and mechanical mechanisms at and around the interface of the formed bond were studied by means of coupled thermo-mechanical FE simulations. Within the framework of material forces the local jump of the Eshelby tensor was compared with the thickness of the formed intermetallic phase for various bonding parameters. This allows us to predict an effective diffusion constant which takes temperature and mechanical driving forces into account. After this relation has been established a subsequent objective of our investigations is to optimize the growth of the Au8Al3 intermetallic phase in terms of bonding parameters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Worldwide, the most common sites of waste disposal are landfills. After solid waste is deposited in a landfill, physical, chemical, and biological processes ensue and modify the waste. Due to these reactions, landfill gas is produced inside the landfill body and effuses into the atmosphere at the outer layer. These processes create environmentally harmful landfill pollutants (methane (CH₄)) and carbon dioxide (CO₂)). The impact of methane on the greenhouse effect is about 20 times higher than that of carbon dioxide.

WorldwideIn order to estimate potential environmental risk of the landfill, a second important phenomenon has to be taken into account: the bacterial methane conversion in the porous cover layer which significantly reduces the amount of methane emitted into the atmosphere. Subsequently, the metabolism of different methanotrophic bacteria converts methane and oxygen into carbon dioxide, water, and biomass.

WorldwideTo model this highly complex and coupled problem we used the well-known theory of porous media to obtain a thermodynamically consistent description which in turn leads to a fully-coupled finite element (FE) calculation concept. The theoretical and numerical framework will be presented in order to describe the coupled processes occurring during the phase transition by bacterial activity in the methane oxidation layer. The model analyzes the relevant gas concentrations of methane, carbon dioxide, oxygen, and nitrogen as well as the driving phenomena of production, diffusion, and convection. Based on a model predicting gas production in landfills, see [1], a multiphase continuum approach for landfill cover layers is presented. In order to validate the model, we compare numerical simulations with experimental data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Due to the scarcity of fossil fuel with a simultaneous rising in global energy demand, it is important to gain access to other energy sources. Geothermal energy holds great potential, and has therefore been studied increasingly in recent years. Within the construction of a geothermal plant, a fluid is introduced via a borehole into the initially gas-filled porous rock. Due the rising pressure gradient, the fluid distributes, displaces the gas and escapes through a second borehole. The modelling approach of these processes in a heterogeneous subsurface proceeds from the Theory of Porous Media (TPM) including an elastically deformable solid, an incompressible fluid, and a gaseous phase [1]. To solve the initial-boundary-value problem, the governing primary variables of the strongly coupled three-phase model are spatially approximated by mixed finite elements, whereas the time-discretisation is carried out by an implicit Euler time-integration scheme. The goal of the presented numerical simulations is to study the specific flow characteristics in a heterogenous subsurface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this note, we present some of our recent work on domain decomposition solvers for the fluid-structure interaction problems with nearly incompressible and anisotropic elasticity models. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Supercritical CO₂ can be injected into deep saline aquifers to reduce the amount of CO₂ in the atmosphere and thus, lessen the impact on the global warming. Qualified reservoirs should be in a sufficient depth to guarantee the thermodynamical environment for the supercritical state of CO₂ and should be confined by an impermeable cap-rock layer. It is crucial to guarantee the safety of the storage site. Therefore, deformation processes and crack development of the rock matrix and the cap-rock layer, which might be induced by the high pressure injection of CO₂, must be investigated. If cracks occur, CO₂ could migrate into shallower regions, where the temperature and pressure cannot support the supercritical condition of the CO₂ anymore. Thus, it is important to describe the phase transition process between supercritical, liquid and gaseous CO₂. The Theory of Porous Media (TPM), see e. g. [1], provides a useful continuum-mechanical basis to describe real natural systems in a thermodynamically consistent way. Hence, the TPM is applied to model multiphasic flow of CO₂ and water and to include elasto-plastic solid deformations of the porous matrix. The Peng-Robinson equation, e. g. [2], is implemented as a cubic equation of state to describe the phase behaviour of CO₂. However, the two-phase region cannot be represented by a continuously differentiable function such as the Peng-Robinson equation and thus, the Antoine equation provides additional information of the vapourisation curve. The Extended Finite-Element Method (XFEM) will be used to account for the discontinuities arising from crack development due to solid deformations [3]. Herein, special attention has to be paid to the matrix-fracture interaction of the fluid phases. Numerical examples are performed to investigate the injection of CO₂ into a saline aquifer. These are computed with the FE program PANDAS, which allows for solutions of strongly coupled multiphasic problems in deformable porous media. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Purpose of this paper is creating of the hypergraphs of the beam concerning of two methods of analysis of vibrating beam by the exact and approximate methods. This approach make possible to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies-poles of beams characteristics. The main subject of the research is the continuous free-sliding (F-S) beam as a subsystems of vibrating beam-system. Findings this approach is a fact, that approximate solutions fulfill all conditions for vibrating beams and can be introduction to synthesis of these systems modeled by hypergraphs. Research limitation is that linear continuous transverse vibrating (F-S) beam is considered. Practical implications of this study is the main point is the introduction to synthesis of transverse vibrating continuous beam-systems. Originality of this approach considers the application Galerkin's method which concerns the analysis of beams and modeling them of transformed hypergraphs. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present contribution is concerned with the macroscopic modelling of the selective beam melting process by using finite elements. In this context the objective is to detail a continuum model to describe the process. Furthermore two different solution approaches are applied to the model and compared in terms of performance. An adaptive mesh refinement strategy is also demonstrated to increase the quality of the solution in the vicinity of the beam. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Paper presents fundamental assumptions of the approximate Galerkin method application in order to vibration analysis of continuous mechanical systems with different form of vibration and different boundary conditions. Flexural vibration of beams, longitudinal vibration of rods and torsional vibration of shafts with all possible ways of fixing were considered. Analyzed mechanical systems were treated as subsystems of mechatronic systems with piezoelectric transducers. This work was done as an introduction to the analysis of mechatronic systems with piezoelectric transducers used as actuators or passive vibration dampers [1–3]. It is impossible to use an exact Fourier method in this case. This is the reason why the approximate Galerkin method was chosen and analysis of its exactness was done as a first step of this work. Dynamic flexibilities of considered mechanical systems were calculated twice, using exact and approximate methods. Obtained results were juxtaposed and it was proved that in some cases the approximate method should be corrected while in the other it is precise enough. A correction method was proposed and it was assumed that the approximate method can be used in mechatronic systems analysis. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work deals with Fluid-Structure-Interaction (FSI) concerning damping characteristics of viscous liquids, which are investigated to make the offshore structures more secure and efficient. On that account, we modeled a damping element prototype consisting essentially of an elastic cover that is attached to the cylindrical mono pile foundation at the height of waves. Within the framework of FSI, the impact of breaking waves on a three-dimensional model of a damping element prototype corresponding to [1] is simulated. In order to measure the influence of different liquid properties on the damping of the impact, the calculations are set up using newtonian and non-newtonian fluids with varying viscosity. For the non-newtonian investigation verification is carried out with a CFD model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present contribution, we investigate and model the flow of a viscous fluid into a single deformable fracture and the associated elastic deformation of the surrounding porous rock. Due to the coupled nature of the problem, conceptually and technically different strategies can be applied to model and solve the resulting hydro-mechanical system. Therefore, two different modeling approaches are analyzed. On the one hand, we derive the governing equations from the conservation of mass avoiding any of the frequently used approximations or simplifications. On the other hand, we describe the physics based on Biot's quasi-static poroelastic equations. We compare and critically discuss the results obtained with the presented different solution approaches. The results show that both models are able to capture the same physical effects, also those caused by the fracture deformation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of this work is to develop a continuum multiphase model to describe infiltration processes for cohesionless soils. For this purpose, a Representative Volume Element (RVE) is considered and described by the continuum mixture theory extended by the concept of volume fractions (Theory of Porous Media – TPM). The thermodynamically consistent TPM is a macroscopical multiphase modeling approach, extended from classical single-phase continuum mechanics. Futhermore a 1-dim example for an infiltration problem is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The contribution is concerned with a finite element formulation that deals with thin structures made from dielectric elastomer material. For that a special solid shell formulation, which uses eight nodes per element and four degrees of freedom (three displacements and one for the electric potential) per node, is presented. It is based on a Hu-Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. In recent years structures made from dielectric elastomers have been investigated by many researchers. This interest is caused by the ability of such devices to efficiently transform electric energy into mechanical work at inexpensive cost of production. The efficiency increases with a higher area to thickness ratio, thus the need to accurately simulate thin structures is well-founded. On the other hand a 3d description of the constitutive behavior is necessary to capture all nonlinear effects arising from the material. Thus a 3d constitutive law with respect to the electro-mechanical coupling incorporated in a finite element solid shell formulation is presented. Some examples demonstrate how it deals with finite strains and large deformations of thin structures by applying electrical loading conditions. The analyzed devices respond with elongation, bending, or buckling, depending on the mode of activation. The electrically induced buckling can be utilized to obtain large deformations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Discrete Element Method (DEM) has been successfully coupled with Computational Fluid Dynamics (CFD) in the framework of OpenFOAM an open source CFD simulation code. In the current study, at first the model is validated with the simple test case of spherical particle comparing the results with the analytical solution. Then the simulation of a gaseous fluidized bed is considered. The coupled mass and momentum balance equations are used to calculate the flow behavior, particle fluidization and bubble formation. The dimensions of the simulation domain are similar to Link et al. (2005) but with different stiffness of particles. The higher velocity of gaseous fluid relative to particles entering through a jet causes the particles to fluidize. The particles behavior, fluidization, bubble formation and the velocity vectors of particles show a good agreement with the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

New multifield materials for the development of smart devices and structures are receiving increasing attentions. Composite materials consisting of piezoelectric and piezomagnetic phases with an additional magnetoelectric coupling effect [1] offer advanced opportunities and may be used for broadband sensing, actuating devices and many other smart devices and structures which are required in engineering sciences. The dynamic crack analysis of magnetoelectroelastic solids is of special importance because such materials are often very brittle and the corresponding results have a direct relevance to the design and optimization of smart structures. The boundary element method (BEM) has been shown to be very attractive and efficient for solving dynamic crack problems in linear magnetoelectroelastic solids [3]. A critical issue in the numerical simulation of crack problems in linear magnetoelectroelastic solids is a realistic description of the mechanical and electromagnetical crack-face boundary conditions, which is considered in this paper. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This article presents a model which describes the chemical decomposition of organic binders, the combined Maxwell-Stefan and Knudsen diffusion and the seepage flow of multiple gaseous reaction products through a porous body and the implementation of the model into a finite element framework. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetic materials have been finding increasingly wider areas of application in industry and therefore, as indicated by the reviews [1], [2] and [3], there is an increased interest in the efficient modeling of such materials that have an inherent coupling between the magnetic and mechanical characteristics. A particular challenge in the modeling of such materials is the algorithmic preservation of the geometric constraint on the magnetization field, that remains constant in magnitude [4]. In earlier works, [5] and [6], we presented a phase field model within a geometrically exact incremental variational framework where the geometric property of the magnetization director is exactly preserved pointwise by nonlinear rotational updates at the nodes. In the current work however, we present an alternative approach that involves an operator split along with a projection step for the magnetization vector. This method provides significant advantages in terms of speed and ease of implementation at the cost of the maximum time step size used. The current work therefore presents comparative study of the the two methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the current contribution, we present a novel method for the determination of the high frequency tortuosity parameter, α_∞ in high porous media. Therefore, time-domain measurements of ultrasonic signals are performed with a transmission technique. Aluminium foams with different pore fluids will be under the scope of experimental investigation. Finally, the experimental results are compared with analytical wave propagation tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling and computation of a process with solid-liquid-solid phase transitions and a free capillary surface is discussed. The main components of the model are heat conduction, a free melt surface, a moving phase boundary, and its coupling with the Navier-Stokes equations. We present two different approaches for handling the phase transitions by applying in a FE method, namely an energy conservation based approach, and a sharp interface approach with moving mesh. By combining both methods, we benefit from the advantages of the respective approach. The methods are applied to a problem where material is accumulated by melting the tip of thin steel wires using laser heating. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

To analyse a composite material with magnetically switchable stiffness properties, the coupling between the magnetic and the mechanical field has to be considered. Here the mechanical as well as the magnetic problem are computed using the eXtended Finite Element Method (XFEM). After a brief introduction of the framework, some results are presented focusing on the ability to calculate correct loads and displacements as well as on convergence rates. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, a phenomenological three-phase model is formulated to simulate agglomeration and breakup of particles contained in a polymer. It shall serve as a starting point for modelling the same phenomena in curing polymers. While isothermal processes are assumed, the model is stated in the framework of continuum mechanics of mixtures. The phenomenological model consists of a polymer phase, and two particle phases. Agglomeration and breakup is modeled as a concentration exchange between the two particle phases. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In modern actuator technology dielectric elastomers are considered as new materials to realize smart actuators which are known as dielectric elastomer actuators (DEAs). In comparison to piezoceramics actuators, DEAs offer the possibility to achieve large deformations with low actuation forces. This property motivates the implementation as artificial muscles since the deformation-force behavior is similar. Other application fields are pumps, deformable surfaces in aerospace, robotics and haptic feedback.

The present work introduces the fundamental concepts to describe the electromechanical coupling in the concept of continuum mechanics for finite deformations.

As a benchmark a 3D sandwich actuator setup is taken into account to analyze the mechanical compression stability of the elastomer structure, see [1, 2]. This structure is also considered to study the influence of inhomogeneities in the deformation behavior. For this purpose piezoceramic and air inclusions are considered in the finite element mesh.

As a last numerical example an elastomer tube with three pairs of electrodes is simulated numerically to motivate the use of dielectric elastomers as peristaltic pumps. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A hydrogel is a polymer network that can absorb a large quantity of solvent and swell due to a physical or chemical stimulus. Hydrogels are more and more used as smart materials in recent micro-applications. This fact requires the development of adequate models and simulation tools for their large deformation behavior. These models must also predict the onset of instabilities, such as folding or creasing. In this work, we study an interesting application of adaptive optical microsystem using a previously developed theory of inhomogeneous large deformation of a pH-sensitive hydrogel. The devices function is based on the swelling of a ring made of a pH-sensitive hydrogel. The latter controls the focal length of the liquid microlens. Our aim is to analyze major design parameters that affect the hydrogel ring behavior and the function of the micro-optical device. The problem is solved numerically with the finite element commercial software ABAQUS. Various modes of large deformation and the influence of the rings aspect ratio on the behavior of the micro-device are investigated. Results show that, for relatively short rings, a stable swelling takes place. Rings with a relatively big aspect ratio can have an unstable swelling with the propagation of a creasing instability. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of the contribution is to formulate an asymptotic model of heat conduction for functionally graded two component laminate reinforced by periodically spaced micro inclusions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present study is concerned with a numerical procedure for prediction of uncertainty effects in sandwich structures with disordered cores. The approach is based on probability distributions of different material properties and their spatial correlation which are the results of the multiple homogenization analysis of testing volume elements. In order to illustrate the essential difference in the results of material uncertainties between computations using random fields and a deterministic approach both methods are applied to a single edge clamped sandwich beam with a metal foam core which is loaded by a force at the free end. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution concerns the mechanics of materials with random network microstructures. It develops a general homogenization approach that allows to link the microscopic deformation of fibers in the disordered network with the macroscopic response of the continuous solid. This link is established by a novel micro-macro relation based on the kinematics of maximal advance paths that constrains the unknown microscopic stretch of fibers with respect to the macroscopic strain. This relation accounts for the topology of the network, in particular, its connectivity and takes for the tetrafunctional networks a clearly interpretable tensorial form. In line with the principle of the minimum averaged free energy the elastic response of the network is obtained by the relaxation of the variable fiber stretch subjected to the kinematic constraint. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Parrinello-Rahman molecular dynamics has proved to be a reliable technique for the investigation of phase transitions in solids. This type of molecular dynamics may lead to a proper description of the atomistic scale in multi-scale analysis of engineering problems. However, the employed Lagrangian is proposed without a derivation and lacks invariance under modular transformations. A re-interpretation of the Lagrangian in terms of continuum mechanics was recently developed. The new formulation is derived in a consistent physical manner and only quantities native to continuum mechanics are incorporated into this Lagrangian. Based on this recent continuum-related derivation, the invariance of the new Lagrangian under modular transformations is investigated. The implication that the obtained dynamics is invariant to the chosen unit cell corroborates with results in solid state physics and is a mandatory requirement for the suitability of multi-scale analysis. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The notion of stress being an inherent continuum concept has been a matter of discussion at the atomistic level. The atomistic stress measure at a given spatial position contains a space averaging volume over nearby atoms to provide an averaged macroscopic stress measure. Previous work on atomistic stress measures introduce the characteristic length as an a priori given parameter. In this contribution we learn the characteristic length directly from the atomistic data itself. Central to our proposed approach is the grouping of atoms with highly similar values of position and stress into the same atomistic sub-population. We hypothesise that atoms with similar values for position and stress are those atoms which harbour the greatest influence over each other and therefore should be contained within the same space averaging volume. Consequently the characteristic length can be computed directly from the discovered sub-populations by averaging over the maximum extent of each sub-population. We motivate the Gaussian mixture model (GMM) as a principled probabilistic method of estimating the similarity between atoms within position-stress space. The GMM parameters are learnt from the atomistic data using the Expectation Maximization (EM) algorithm. To form a parsimonious representation of the dataset we regularise our model using the Bayesian Information Criterion (BIC) which maintains a balance between too few and too many atomistic sub-populations. We use the GMM to segment the atoms into homogeneous sub-populations based on the probability of each atom belonging to a particular sub-population. Thorough evaluation is conducted on a numerical example of an edge dislocation in a single crystal. We derive estimates of the space averaging volume which are in very close agreement to the corresponding analytical solution. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE² approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical aspects of two-scale modeling of epoxy/glass composites are presented. The homogenization process is carried out under consideration of periodic boundary constraints (PBC) of the representative volume element (RVE) due to the periodic structure of glassfiber reinforced epoxy systems. The introduction of artificial constraints for computing macro-stresses and macro-moduli is presented by giving the modified algorithmic treatment of a two-scale approach using PBC. The proposed algorithm is applied to an ISO 527 epoxy/glass test specimen. The results of computations considering or not considering interphases and interfaces within the composite are compared. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present study is concerned with a numerical scheme for prediction of the effective properties of solid foams considering their uncertainty. The approach is based on an analysis of a large-scale, statistically representative volume element which is subdivided into small-scale testing volume elements. Application of a standard homogenization scheme to the testing volume elements together with a stochastic evaluation yields a complete probabilistic characterization of the material which may be used for a random field definition of the material behaviour in a macroscopic effective field analysis of foam structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution presents a method to construct three-dimensional Statistically Similar RVEs (SSRVEs) for the simulation of dual phase steel (DP steel). Since the microstructure of DP steel strongly influences the overall material properties, it should be incorporated in numerical calculations. For this purpose the FE² method can be applied and for an efficient computation SSRVEs with a reduced complexity compared to the real microstructure have to be defined, which still represent the mechanical response of the material accurately. The construction method is based on the minimization of a least-square functional considering suitable statistical measures describing the inclusion morphology of a given real microstructure. The mechanical response of the SSRVEs is compared to the response of the real microstructure in virtual mechanical tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A stochastic homogenization scheme for the computation of effective elastic properties for damaged micro-heterogeneous materials is presented. The statistics is captured by uncertain material properties as well as stochastic interpolation between the upper and lower Hashin-Shtrikman bounds. The resulting multidimensional stochastic problem is solved via sophisticated Monte Carlo methods and applied to Ultra-High-Performance-Concrete. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of this contribution is to present a new method of formulation of simplified model of skeletonal structures. The exact description of the heat conduction leads to PDEs with highly oscillating and discontinuous coefficients. We would like to obtain the simplified models of the tolerance type which is described by PDEs with smooth coefficients. As a method of modelling we used the tolerance averaging. This method could be treated as a certain generalization of the well known homogenization method. However, it is not basis on the limit passage from the microstructure size to zero. This method makes it possible to analyze the effect of microstructure size on the overall i.e. macroscopic behavior of the composite structure. Instead of limit passage, we introduce here the concept of tolerance parameter. Using this concept we could define the slowly varying functions [1], [2]. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The contribution deals with the modeling of two phenomena that are characteristic of the curing of polymers, namely the increasing viscosity and the volume decrease known as autogeneous shrinkage. Both of these processes are caused by the crosslinking of polymer chains during polymerization. In order to model the viscoelastic effects, the free energy consisting of an equilibrium and a non-equilibrium part is proposed. The former is related to the elastic processes and depends on total deformations. The latter is caused by the viscoelastic effects and only depends on the elastic part of deformations. In order to avoid volume locking effects typical of isochoric materials, both parts of the free energy density are furthermore split into a volumetric and a deviatoric part. A multifield description depending on the displacements, volume change and hydrostatic pressure is introduced as well. Different from the viscous process, the modeling of shrinkage effects does not require a new assumption for the free energy but a split of the total deformation gradient into a shrinkage and a mechanical part. The model suitable for simulating both of the mentioned phenomena is implemented in the single- and multiscale FE program. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using porous hyperelastic material model. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The new material model which is based on Danielsson et al [1] decouples the influence of porosity from the mechanical properties of the solid material by introducing volume fraction of the pores as an explicit scalar variable. The finite element simulations are then followed by experiments on complex model to validate the material model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

When dynamic problems are of interest, the high-frequency waves reflected from the coupling boundary will pollute the solution in the MD domain quickly and render the results from the multiscale model meaningless. In this contribution, we show that by applying artificial damping only to the high-frequency part of the displacement field in the coupling domain in the weak coupling method can significantly reduce the reflections in the MD domain while not affecting the low-frequency part that can be transmitted into the FE domain. The frequency analysis shows the errors in the magnitudes and phases of wave components are orders of magnitudes smaller than that in the bridging domain model or undamped weak coupling model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The characteristics of polymers such as force-deformation behaviour, strength, fatigue and wear resistance, can be tailored by embedding it with filler particles. The influence of the fillers on the material behaviour significantly depends on the size and geometric form of the filler aggregates, which vary under mechanical loading. The concept of super element is used to model filler particles. This is now coupled with the polymer matrix to generate a finite element model of filler reinforced polymers. In this work, we investigate the effect of filler geometry and volume fraction of fillers on the overall stiffness of the filler reinforced polymer. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A brittle damage model based on multiscale considerations and homogenisation procedures is presented. Cell models are developed as RVE including different microstructural features. The material laws themselves are formulated on the continuum level. Local failure occurs if the damage variable reaches a critical value. For simple configurations of the microstructure, the relation between stress, strain und temperature is derived from analytical considerations. In order to properly model the thermo-mechanical coupling, the temperature-dependence of material constants is taken into account. Fracture and damage mechanical approaches are combined using different techniques. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Wave propagation is used in many fields for measurement and characterization. Corresponding multiphase models usually use a continuous approach. Nevertheless, systems like wetted rocks may be saturated residually in certain situations. In such cases, one fluid is distributed as clusters, each different in size and shape. One single, continuous phase cannot account for a variety of fluid clusters, either disconnected from each other or connected only about thin liquid films. Therefore, we present a model that considers a heterogeneous distribution of disconnected fluid clusters in the form of harmonic oscillators. These oscillators are described and distinguished by their mass, damping and eigenfrequency. Hence, the model allows to characterize different clusters and includes an additional damping mechanism due to oscillations of the fluid clusters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

One of the main challenges using the Discrete Element Method is that there is no direct compliance to the well known continuum parameters such as elastic moduli. In this article we show how homogenization procedures using representative volume elements composed of discrete particles lead to Cosserat continua.

Simulating a shear test with discrete elements it becomes obvious, that the evolving microstructure is mainly composed of contact chains that form triangles and quadrilaterals. For these contact chains we set up contact energies in normal and shear directions and combine those to derive the effective energy of the material. By comparison of this energy to a Cosserat energy we can derive formulas for the Lamé and Cosserat parameters. They are now only dependent on the interaction energies and radii of the particles. To show the validity of our assumptions and derivations we present some discrete element simulations of shear tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

What is the contact condition in a 1D beam-model and is it possible to obtain the frictional moments and forces from the 3D traction? If it is possible does the cross-section of the beams influence these values? These questions motivate to study the dimension reduction of a 3D contact problem for beams. This paper is a continuation of [1]. In [1] the asymptotic dimension reduction of a Robin-type elasticity boundary value problem was presented. In this work the explicit relation between a 3D contact problem and a 3D Robin-type elasticity boundary value problem are established and the 1D equations derived in [1] are interpreted as 1D contact conditions, further some numerical examples are shown. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

By analysing the facet structure of the convex polytope generated by the twelve transformation strains of cubic to monoclinic-I martensite, we show that there are two different kinds of monoclinic-I martensite. These two kinds differ in the sign of a material parameter. While the symmetry properties of both kinds are the same, the geometrical structure of the set of recoverable strains is different. A key idea is to consider the convex polytope formed by the transformation strains and to study its facets. Another insight is to use invariant theory to exploit the fact that compatible cones are algebraic surfaces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work multiscale failure modeling of composites is made using generalized finite element method (GFEM). In this method the global approximation are constructed by combining the local basis with partition of unity functions. The enrichment functions for the GFEM approximation are computed using a proper orthogonal decomposition (POD) technique. The approximation is then used in a two scale Galerkin scheme for failure modeling of composites. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present work a mixed finite element based on a least-squares approach (LSFEM) is proposed. We consider a formulation for Newtonian fluid flow, which is described by the incompressible Navier-Stokes equations. The starting point is a div-grad three-field first-order system with stresses, velocities, and pressure as unknowns. Following the idea in CAI et al. [1], this three-field formulation can be transformed into a reduced stress-velocity (s-v) two-field formulation, which is the basis for the associated minimization problem. In order to show the applicability of the considered approach a numerical example is presented at the end of the paper. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Blade element momentum (BEM) theory which is based on the two-dimensional (2D) aerodynamic properties of airfoil blade element is the most common computational engineering method for the prediction of loads and power curves of wind turbines. Although most BEM models yield acceptable results for high tip-speed ratios where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the loads and power in stall regime for stall-controlled turbines. Understanding of the stall delay phenomenon on wind turbines remains, to this day, incomplete. The lack of a conceptual model for the complex three-dimensional (3D) flow field on the rotor blade, where stall is begins, how it progresses and where stall is practically terminated, has hindered the finding of a unanimously accepted solution. The paper aims at giving a better understanding of the delayed stall events and a reasonably simple correction model that complements the 2D airfoil characteristics used to a BEM method. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Steady two-dimensional laminar flows past an expansion ramp are known to exist up to a critical ramp angle in the limit c as the Reynolds number tends to infinity. The theory of viscous-inviscid interaction combined with a local bifurcation analysis is used to study the evolution of three-dimensional unsteady perturbations if for both sub- and supercritical conditions. Special emphasis is placed on the effects of controlling devices and the phenomenon of bubble bursting. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The appearance of short laminar separation bubbles in high Reynolds number (Re) wall bounded flows due to appropriate adverse pressure gradient conditions is usually associated with minor effects on global flow properties (e.g. lift force). However, localized reverse flow regions are known to react very sensitively to perturbations and in further consequence may trigger the laminar-turbulent transition process or even cause global separation. The present investigation of marginally separated boundary layer flows is based on an asymptotic approach Re → ∞. Special emphasis is placed on solutions of the corresponding model equations which blow up within finite time indicating the ejection of a vortical structure and the emergence of shorter spatio-temporal scales reminiscent of the early transition scenario (‘ bubble bursting’ ). Within the framework of marginal separation theory, an alternative adjoint operator method is used to formulate evolution equations governing the viscous-inviscid interaction process in leading and higher order correction required for the study of later stages of the flow development. Their blow up structure specifies the initial condition of and the match to the subsequent triple deck stage. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, a theoretical study of the turn manoeuvre of an agricultural aircraft is presented. The manoeuvre with changeable altitude is analyzed, together with the effect of the load factors on the turn manoeuvre characteristics during the field-treating flights. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We investigate the electrokinetic flow in microchannels with internal electrodes. Experiments and numerical simulations are performed. The micro–particle–image velocimetry method is used to measure two–dimesional, two–component velocity fields over the complete height of the microchannel. Based on this measurements, the third velocity component, which cannot be measured directly, is calculated by an integration of the continuity equation. Due to the fact that microparticles, used for the μPIV are electrically non-neutral leads to the problem that these particles experience electrophoretic forces. That means that the particle movement appears to be a superposition of electroosmotic and electrophorectic effects. To verify the influence of electrophoretic effects on the microparticles, additional numerical calculations are made. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The conditional analysis of the instantaneous wall friction is applied on time records made in transitional boundary layers originating on smooth surface or surface covered by sand paper (grits 60) under turbulent free stream. The applied intermittency analysis of measurement allowed the evaluations of turbulent and non-turbulent zone averages. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper a method is presented to optimize the number of particles in three-dimensional computations using the SPH method, based on the nearest neighbour. The process is presented for the breaking dam problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A well known and often used method to obtain anisotropic polymer films is the so-called pressing process. Here, films are squeezed under high temperatures, pressure and deformation rates. To simulate such a process, the polymeric matrix is treated as a non-Newtonian, viscoelastic melt. The modeling of such melts is done with the anisotropic molecule movement tensor generalization of the Maxwell Model for high deformation rates. The viscoelastic flow simulations are done with DEVSS stabilization techniques and an ALE based dynamic mesh Method. In this work we present simulations in order to show the difference between classical approaches using a generalized Newtonian viscosity to model the melt and the used viscoelastic models. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of Interphase Mass Transfer (IMT) on the unsteady convective diffusion in a fluid flow through a tube surrounded by a porous medium is examined against the background of no IMT. The three coefficients namely exchange coefficient, convection coefficient, and dispersion coefficient are evaluated asymptotically at large-time. The exchange coefficient exists due to IMT. All-time analysis is made analytically when there is no IMT. The mean concentration distribution is measured at a point inside and outside the slug. The peak of mean concentration is higher than that of pure convection and it is further enhanced with increase of porous parameter. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In-line separation of suspensions can become difficult in case of particles with comparable values of densities. For flows in micro devices in such cases gravitational settling is inefficient, and other separation techniques must be applied. In case of magneto active particles, the action of Kelvin magnetic force in a non-uniform magnetic field could be used in order to achieve a higher degree of particles separation. The contribution therefore deals with Euler-Lagrangian formulation of dilute two-phase flows. The Boundary element based computational algorithm solves the incompressible Navier-Stokes equations written in velocity-vorticity formulation. The non-uniform magnetic field is defined analytically for the case of a set of long thin wires. The particle trajectories are computed by applying the 4th order Runge-Kutta method. The computed test case consists of a narrow channel with laminar flow of suspension under Re = 1 − 10. Particle trajectories under the influence of a non-uniform magnetic field are computed for the case of magnetite and aluminium particles suspended in water. The efficiency of separation on basis of particle trajectories for different values of Re number and magnetic field strength is performed, clearly indicating superior separation of magneto active particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The plane stagnation flow onto (Hiemenz boundary layer, HBL) and the asymptotic suction boundary layer flow over a flat wall (ASBL) are two boundary layer flows for which the incompressible Navier-Stokes equations are amenable to exact similarity solutions. The Hiemenz solution has been extended to swept Hiemenz flows by superposition of a third, spanwise-homogeneous sweep velocity. This solution becomes singular as the chordwise, tangential base flow component vanishes. In this limit, the homogeneous ASBL solution is valid, which however cannot describe the swept Hiemenz flow, because it does not contain any chordwise velocity. This work presents a generalized three-dimensional similarity solution which describes three-dimensional spanwise homogeneously impinging boundary layers at arbitrary wall-normal suction velocities, using a rescaled similarity coordinate. The HBL and the ASBL are shown to be two limits of this solution. Further extensions consist of oblique impingement or different boundary suction directions, such as slip or stretching walls. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The knowledge of the fluid behaviour in inclined cavities is of fundamental importance as far as heat and mass transfer are concerned. The interest in this subject is particularly increasing due to the rapid process in micro technologies. We therefore studied the flow- and temperature field of such flows numerically as well as experimentally using CFD and PIV/T, respectively. We present and discuss the numerical and experimental results of our investigations and explain the applied techniques. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work present a numerical study of the non isothermal flow of metal in the semi-solid state in the shot sleeve of horizontal die casting machine during the injection process. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The flow characteristics and stall delay phenomenon of a stall regulated wind turbine rotor due to blade rotation in steady state non-yawed conditions are investigated. An incompressible Reynolds-averaged Navier-Stokes solver is applied to carry out the separate flow cases at high wind speeds from 11 m/s to 25 m/s with an interval of 2 m/s. The objective of the present research effort is to validate a first-principles based approach for modeling horizontal axis wind turbines (HAWT) under stalled flow conditions using NREL/Phase VI rotor data. The computational results are compared with the predicted values derived by a new stall-delay model and blade element momentum (BEM) method. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A gas exchange model based on diffusion and stack pressure driven convection for display cases will be discussed and evaluated experimentally. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Flow separation can be viewed as one of the trigger events of laminar-turbulent boundary layer transition. Thus, intensive investigations have been carried out as to when and how laminar boundary layers break down. In the special case of marginal separation, i.e. the formation of short laminar separation bubbles, high Reynolds number asymptotic theory yields integro-differential equations governing the essential flow behavior. We will present further considerations of associated initial value problems (IVPs) in planar and three-dimensional flow cases regarding the general ill-posedness. As for regularization methods, higher order asymptotic terms comprising the streamline curvature in the boundary layer region are taken into account rendering the hence modified problem well-posed, which can be seen from the dispersion relation and numerical solutions of the full problem. Even though the regularized IVPs admit limiting steady states in their time evolution, the phenomenon of finite time blow-up, which can be interpreted as “bubble bursting”, is still present for certain initial conditions. The inevitable breakdown of the asymptotic description leads to the emergence of a new asymptotic structure of shorter spatio-temporal scales associated with the unique self-similar blow-up structure. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Internal fluid flow behavior for slow moving small droplets in contact with hydrophobic surfaces is analyzed. The shape of the droplet is first computed using the Young-Laplace equation. For this purpose a Finite Element (FE) model [1], in which contact constraints are enforced through Penalty and Augmented Lagrange Multiplier methods, is used. The flow field within the droplet is then analyzed using the Stokes flow model, considering a de-coupled approach. Similar to the membrane deformation model, the formulation for the flow analysis is also expressed in the framework of FE analysis. Both, stabilized (Pressure Stabilizing/Petrov-Galerkin PSPG) and Galerkin FE formulations are considered. The motion of the fluid inside the droplet is governed by the slip condition enforced on the membrane of the droplet. Numerical examples for droplets rolling steadily are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

One of the simplest models for the velocity distribution in a pipe cross-section dependent on two parameters consists of two layers of different thickness and velocity. Unfortunately relative thickness and velocity of the wall layer cannot be expressed analytically in terms of Truckenbrodt's energy and momentum coefficents. But relative thicknesses of a three-layer model with wall and intermediate layer having opposite core and zero velocity can be. Reasonable in case of strong reverse wall flow only they allow a crude estimate of the parameters of the two-layer model, which may then serve as initial values in computing them iteratively. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An interaction of the free turbulent shear flow and the steady temperature field, which develops to the homogeneity, was studied. The temperature field was generated by parallel thin heated wires. The isotropic grid turbulence is supposed. Heated wire generates large cross temperature gradients and development of the temperature field was investigated experimentally. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. At the stage of vortex breakdown the flow is dominated by a conical shear layer and a large recirculation zone around the jet axis. We performed Large-Eddy Simulations (LES) of compressible swirling jet flows at Re=5000, Ma=0.6 in the high swirl number regime (S=1). A nozzle is included in our computational setup to account for more realistic inflow conditions. The obtained velocity fields are analyzed by means of temporal and spatial dynamic mode decomposition (DMD) to get further insight into the characteristic structures dominating the flow. We present eigenvalue spectra for the case under consideration and discuss the stability behaviour in time and space. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Turbulence structure of swirling flows is being investigated in this paper, on the basis of experimental, self conducted measurements, and theoretical and numerical results. Turbulent swirling flows are extremely inhomogeneous, three dimensional and anisotropic. The aim of this paper is to investigate significant influence of swirl onto statistical parameters and non-gradient turbulent transfer. Contemporary optical measuring techniques two component laser Doppler anemometry (LDA) and stereo particle image velocimetry (SPIV) have been applied. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A multiscale approach describing a turbulent flame as a gasdynamic discontinuity [1] on each scale is proposed. The methodology becomes attractive if simulations on individual scales are implemented in a very efficient way. Simulations in a 2D rectangular box with an artificial turbulence field exploiting a robust phase-field/level-set method fit this purpose. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Flow structure behind the backward facing step in a narrow channel was studied in details. The step height was 25% of the channel width. The structure of the region just behind the step forming the back-flow region is studied in details using stereo PIV technique. Time-mean 3D structures behind the step are evaluated and shown in the paper. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The paper presents results of Direct Numerical Simulation of bubbly flow to analyse the interaction between the turbulent fluid and the bubbles. The simulations aim to investigate the effect of the bubble Reynolds number, related to the bubble size, and the void fraction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The paper reports on direct numerical simulations of a particle-laden open channel flow carried out to investigate the interaction between the dispersed and the continuous phase. The dispersed phase is represented by an immersed boundary method. The particle-particle collisions are accounted for by a physically motivated collision model. Two cases, one with shear stress below the threshold of mobilization and the other with shear stress above the threshold are considered. The different density ratios lead to different types of modification of the flow field by the formation of density-specific patterns of the particles. Light particles do not attain resting states but saltate evenly distributed in span-wise direction. Heavy particles tend to form stream-wise clusters of inactive particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

It has been known for a long time that the introduction of a small amount of polymer additives could significantly reduce friction drag in wall-bounded turbulent flows [1]. However, in the last years also the effect of polymers on turbulent thermal convection has drawn attention with controversial results. In this context, aim of this contribution is the presentation of the mathematical model for the study of natural convection between parallel walls in a dilute polymer solution. The discussion here will be also extended to the description of the kinetic and free energy balances in this flow. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work concerns numerical simulation of free-surface flows of highly viscous liquids in single-screw extruders.The numerical treatment of a partially filled extruder is a challenging task due to the complex geometry and the large differences in density and viscosity between the two phases, e.g. polymer melt and air. Furthermore, the rotation of the screw leads to a continuous renewing of the free-surface. For this purpose the Volume of Fluid (VOF) method is used. First a simplified two-dimensional model of a single-screw extruder is considered. Good agreement is obtained between the numerical results and experimental data. Finally, the three dimensional free-surface flow in a partially filled single-screw extruder with dynamic mesh motion is presented. In addition, the power characteristics of a conveying screw element with varying degree of filling is discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The great advantages of micro–reactors are associated with an extremely high surface–to–volume ratio. Hence, micro–reactors permit promising operating conditions, such as almost perfect heat or mass transfer. The hydrodynamics of a liquid/liquid slug flow in a micro–channel is characterized by complex vortex structures in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persists between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner. To study the physics of this complex liquid/liquid system, a modified level–set method in conjunction with an immersed–boundary formulation is engaged. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The objective of this study is to model the primary breakup of a plane liquid sheet emerging from an air-blast nozzle. In the present work the interface compression scheme proposed by OpenCFD Ltd. [1] has been used to capture the interface between the liquid and gas. A One-equation subgrid scale (sgs) turbulent energy transport model attributed to Yoshizawa [2] is used for modeling the effects of turbulence. The set up case selected for this study is based on the experiments carried out by Mitra [3]. The 2D simulations performed in this study predict the breakup length of the plane liquid sheet in good agreement with the experimental data. Future work will involve, performing 3D simulations of the plane liquid sheet generated by the air-blast nozzle and performing comparisons of the resulting droplet characteristics with the experimental data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present a finite element method for the flow of two immiscible incompressible fluids in two and three dimensions. Thereby the presence of surface active agents (surfactants) on the interface is allowed, which alter the surface tension. The model consists of the incompressible Navier-Stokes equations for velocity and pressure and a convection-diffusion equation on the interface for the distribution of the surfactant. A moving grid technique is applied to track the interface, on that account a Arbitrary-Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equation is used. The surface tension force is incorporated directly by making use of the Laplace-Beltrami operator technique [1]. Furthermore, we use a finite element method for the convection-diffusion equation on the moving hypersurface. In order to get a high accurate method the interface, velocity, pressure, and the surfactant concentration are approximated by isoparametric finite elements. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution, the friction at atomical scale has been investigated by using molecular dynamics (MD) simulations. This work surves as a preliminary study on the influence of surface texture on the friction at atomic scale, where simple rectangular grooves are added to the contact surface. Our results suggest definite dependence of the friction on the orientation of the grooves, which decreases as the velocity increases. For a given velocity, an optimal direction of sliding which gives the minimum averaged friction coefficient can be identified. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Thin droplets spreading on a solid substrate are investigated, with a special focus on temperature effects. The aim is to manipulate the fingering instability which may occur in the spreading in a spin coating process. The analysis bases on lubrication approximation, valid for flat thin droplets, which usually is the case. The dynamic of the wetting is implemented by using a generalized law of Tanner, coupling the contact angle (CA) of the droplet at the (apparent) contact line (CL) with its speed. A one-way coupling is used to investigate, whether viscous heating has to be taken into account. It can be derived that its role is negligible in the spreading process of a thin droplet, even for a relatively large viscous influence (large capillary number). Analyzing the results of a linear stability analysis of the fingering instability and taking Marangoni-stresses (MS) into account reveals, that the instability may be suppressed by cooling the ambient gas or heating the substrate during the spreading. Unfortunately an comparison with experiments for spreading droplets in a heated gas shows deviations for larger spreading radii. The influence of temperature on density is investigated and on the way a criteria, from which it may be obtained whether a simple Boussinesq-approximation (BA) is appropriate or not. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present work the complex process of diffusion-controlled wet chemical etching of a rotating silicon wafer is analyzed in the framework of an unsteady integral boundary layer approximation. The obtained results reproduce the waviness and the associated enhancement of the mass transfer in the wavy region, and are in good agreement with experimental findings. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The existing combinatorial methods for iso-surface computation are efficient for pure visualization purposes, but it is known that the resulting iso-surfaces can have holes, and topological problems like missing or wrong connectivity can appear. To avoid such problems, we introduce a graph-theoretical method for the computation of iso-surfaces on cuboid meshes in ℝ³. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Deeper investigation of time discretization for free surface problems is a widely neglected problem. Many existing approaches use an explicit decoupling which is only conditionally stable. Only few unconditionally stable methods are known, and known methods may suffer from too strong numerical dissipativity. They are also usually of first rder only [1, 9]. We are therefore looking for unconditionally stable, minimally dissipative methods of higher order.

Linearly implicit Runge-Kutta (LIRK) methods are a class of one-step methods that require the solution of linear systems in each time step of a nonlinear system. They are well suited for discretized PDEs, e.g. parabolic problems [7]. They have been used successfully to solve the incompressible Navier-Stokes equations [5]. We suggest an adaption of these methods for free surface problems and compare different approximations to the Jacobian matrix needed for such methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution deals with the coupling of compressible to incompressible flow regions in one space dimension. Iterative coupling procedures based on jump conditions across the interface have been derived. They couple the solution of a half Riemann problem on the compressible side to the analytical solution of the incompressible side. For the incompressible equations, the pressure is split into a thermodynamic background and a hydrodynamic part. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Sediment transport involves fluid flow in two different regions. In the free flow domain, the flow is governed by the viscous Newtonian fluid; sediment only occurs as suspended particles. In the porous domain however, the flow is governed by the pore geometry of the porous skeleton consisting of sedimented grains. In nature, the interface between these two domains is not a no-slip boundary for the free flow. In this study, we quantify how sediment transport is affected by the interaction of the two different flows. We do this by comparing fluid flow in no-slip bounded flow channels to fluid flow in channels containing both a free and a porous domain. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper a method is described to simulate isobaric multiphase flows at low Mach numbers with steep temperature gradients for fluids with non-negligible thermal expansivity. Governing equations and solution procedure are outlined. Further, a test case is shown in order to verify the model. Single phase natural convection flows with large temperature differences and either constant or temperature dependent transport properties were simulated to prove the solution of coupled Navier-Stokes and energy equations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Homogeneous ice nucleation in supercooled water is studied with the classical nucleation theory (CNT). The nucleated ice particles are assumed to possess physical properties of metastable cubic ice. The comparison with literature data on homogeneous ice nucleation rates shows a good agreement between CNT predictions and experimental nucleation rates. The CNT predicted nucleation rate, critical cluster radius, and critical nucleation work are parametrized for use in numerical simulations of the freezing process of supercooled water droplets. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper a numerical approach, based on the Scaled Boundary Finite Element Method (SBFEM), is described to obtain dispersion relations for propagating modes in wave guides. While the formulation is developed for plate structures, it can easily be extended to wave guides with arbitrary cross-section. The cross-section is discretized in the Finite Element sense while all equations remain analytical in the direction of propagation. The wave numbers of all propagating modes are obtained as the solutions of a standard eigenvalue problem. The group velocities can be calculated accurately as the eigenvalue derivatives. The use of higher-order elements drastically increases the efficiency and accuracy of the computation. This approach can be used for wave guides with arbitrary distribution of material parameters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In order to localize cracks in cylindrical structures using guided waves, precise knowledge of the wave speeds is crucial. Instead of basing calculations on crisp parameters, for this Structural Health Monitoring application, uncertainty in parameters is handled by representing parameters as fuzzy numbers and applying the Transformation Method. For calculating dispersion curves, the Waveguide Finite Element Method is used for each parameter set. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For the simulation of the interaction of elastic waves in CFRP Plates with inhomogeneities and defects the spectral finite element method (SEM) is under investigation. The SEM uses high-order shape functions which are composed of Lagrange polynomials with nodes at the Gauss-Lobatto quadrature (GLq) points. In this way we obtain a diagonal mass matrix which makes an explicit time scheme more efficient. In a numerical example based on the first order shear deformation theory (FSDT) a computation by FEAP of an interaction with an inhomogeneity is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A numerical simulation setup is presented which allows to study a circular jet flow configuration in which the nozzle is included in the simulation domain. Direct Numerical Simulations (DNS) are performed using up to 10^th order compact finite-difference schemes which are stabilized by applying a mild low-pass filter. A parallelization approach has been implemented which shows good weak and strong scaling behavior. At the inflow the Synthetic Eddy Method is employed to generate turbulent fluctuations in the nozzle boundary layer with prescribed statistics, which are imposed by a sponge (forcing) layer technique. Simulation results for the jet flow field obtained at Reynolds number Re_D = 19000 and a Mach number Ma = 0.9 as well as for the acoustic near-field are found to be in good agreement with recent nozzle-jet simulation results as well as experimental findings. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Structural Health Monitoring (SHM) allows the integrity of a system to be monitored in situ, detecting weaknesses as they form. Due to the waveguide nature of cylindrical structures, ultrasonic waves can be used to detect defects in cables over large distances. Considering that common power line cables consist of several individual wires, a straightforward energy-based approach is chosen to simplify the model development. The purpose of this investigation is to extend the current coupling model to include n wires and to verify this model for a seven-wire cable, experimentally. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, an inverse acoustical characterization for determination of porosity, flow resistivity, tortuosity and other parameters of a concreted wood material was proposed. Sound absorption measurements for a concreted wood fiber material were made in an impedance tube. Four acoustical models from literature were briefly described. Each model was fitted to the experimental data in order to compute their unknown parameters. Using a least-square method, the experimental data (sound absorption coefficient) was used to optimize the acoustical models by best-fitting the unknown parameters. The results of this paper show that the presented technique leads to reliable estimates of the physical parameters of the material. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Piles are widely used to build a proper foundation for various buildings. The pile's quality in situ can be tested by a so called pile integrity test. In order to apply this test, an acceleration sensor is attached to the pile's head which than receives an impulse. Due to this impulse a p-wave runs through the pile. The major part of this wave is reflected from the pile's toe and is measured by the attached acceleration sensor on top of the pile. This yields an acceleration-time plot which has to be analysed to determine the pile's condition.

Sometimes the interpretation of these plots is difficult, specially when the cross-section of the pile is changing or is influenced by the surrounding soil. For a better understanding of this kind of measurements, numerical simulations can be performed. For these simulations a coupled finite element method (FEM) and scaled boundary finite element method (SBFEM) approach is used. This approach satisfies Sommerfeld's radiation condition and allows simulating an infinite half-space. This ensures that the applied impulse will not to be reflected at the artificial boundary which is introduced by the boundary of the numerical discretisation. The coupled approach proposed here requires discretisation of a small domain only in contrast to a purely FEM-based approach. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper presents a constructive variant of acoustic impedance tube used to determine the coefficient of sound absorption materials. This alternative design brings a contribution in terms of the number of microphones mounted on the tube impedance control of acoustic vibration generator, with the calibration system of microphones mounted on the device. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Ultrasonic waves travel in rope structures over long distances as guided waves, allowing for effective health monitoring. In order to localize and characterize defects, an exact knowledge of the propagation, reflection, and transmission properties of the ultrasonic waves is required. These properties can be obtained using the Finite Element Method by modeling a segment of the periodic waveguide with a periodicity condition. The solution of the corresponding eigenvalue problem leads to all propagating modes of the waveguide as well as locally generated evanescent modes. The Boundary Element Method (BEM) is used in combination with the Finite Element Method for characterizing the wave propagation. The mode conversion at discontinuities, such as cracks or notches, can be subsequently described by reflection and transmission coefficients. The simulation results are the corresponding coefficients as a function of frequency and enable the selection of adequate modes for an effective defect detection. Additionally, it is demonstrated that along with the localization of cracks, conclusions about the crack geometry can be made with the help of reflection and transmission coefficients. The reliability and numerical accuracy of the simulation results are verfied by comparison with experimental findings. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Sound emission is nowadays considered as a major environmental issue. The sound emission is generated, amongst other sources, due to an increasing amount of traffic and transport, i.e. road transport, rail and air traffic. Here, sound emission presents a significant risk to public health and a major cause of stress, especially in industrial countries. In this framework the present work is dedicated to the topic of active noise control with the target of noise reduction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Wave propagation in highly porous materials has a well established theoretical background. Still there are parameters which require complex laboratory experimentation in order to find numerical values. This paper presents an effective method to calculate the tortuosity of aluminum foam using numerical simulations. The work flow begins with the acquisition of the foam geometry by means of a micro-CT scanner and further image segmentation and analysis. The elastodynamic wave propagation equation is solved using a velocity-stress rotated staggered finite-difference technique. The effective wave velocities are calculated and using the fluid and, aluminum effective properties, the tortuosity is determined. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Topology optimization is used to optimize problems of flow around bodies and problems of guided flow. Within the context of research, optimization criteria are developed to increase the energy efficiency of these problems [1] [2] [3] [4] [5]. In order to evaluate the new criteria in respect to the increasing of energy efficiency, reference bodies for different Reynolds numbers in combination with given design space limitations are needed. Therefore, an optimal body at Reynolds number against 0 was analytically determined by Bourot [6]. At higher Reynolds numbers, in the range of laminar and turbulent flows, no analytical solution is known. Accordingly, reference bodies are calculated by CFD calculations at three technical relevant Reynolds numbers (1.000, 32.000, 100.000) in combination with parameter optimization. The cross section of the bodies is described by a parameterized model.

To get the optimal body, a parameter optimization based on a “brute force”; algorithm is used to optimize with regard to the friction loss and pressure loss in order to minimize the total loss (c_d-value). The result is an optimal parameter constellation, depending on the Reynolds number. Within the results, it is possible to develop the optimal geometries. The identified characteristics of the flow field around these bodies are used as base for new optimization criteria. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Beer fermentation is a very complex process, especially in the fluid-mechanical and the biochemical point of view. Our aim is to optimize the fermentation by flow control, which requires quantities of data. The applied velocity measuring techniques should be non-invasive to ensure that neither the flow nor the fermentation in the green beer gets influenced. Therefore, an Ultrasonic Doppler Velocimetry (UDV) system is used to determine velocity fields with 128 measuring points. It works in the turbid fluid with the existing yeast cells as tracer particles and can be applied easily to the industrial scale.

For the validation of CFD-codes and the better understanding of measurements and flow processes, model fluids are used. They can be adapted to real fluid properties like density and viscosity and allow measurements with Laser Doppler Anemometry (LDA). Another advantage over the real fluid is their fixed composition, which leads to negligible natural variations. All experiments are performed in a 270 litre fermenter. Besides the real process, measurements through optical access points and the simulation of fermentations with CO₂ and heat emission are enabled. Eight individually controllable cooling zones are used as thermal actors. Resulting changes in boundary conditions induce temperature gradients and hence allow to control the flow inside the tank.

This work deals with the experimental set-up and the results on the one hand and a comparison between real and simulated fermentations on the other hand. Special attention is given to investigations of the multi-phase flow inside the vessel and the effects of changing constraints. The usability of UDV measurement techniques is the key benefit in this case, because it can be used in green beer and model fluids and does not influence the flow. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A numerical method is developed to study the stabilizing effect of dielectric barrier discharge plasma actuators on laminar boundary-layer flow. A finite difference approach based on a Keller box discretization is chosen to solve the Falkner-Skan transformed boundary-layer equations. The fluid dynamic effect of the flow-control device is implemented as a body-force field, derived quantitatively from previous measurements using particle image velocimetry. The resulting laminar boundary-layer flow is compared to experimental wind tunnel measurements and the effect on hydrodynamic stability is investigated in the framework of linear stability theory. A good agreement between experimentally acquired and numerically predicted transition locations based on an empirical function is obtained, rendering the numerical scheme valuable as a design tool for DBD based flow control applications. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The question whether large turbulent drag reduction can be achieved at the high values of Re typical of applications is addressed. Answering such question, either by experiments or DNS, is obviously challenging. For DNS, the problem lies in the tremendous increase of the computational cost with Re, that has to be appreciated in view of the need of carrying out an entire parametric study at every Re, owing to the unknown location of the optimal forcing parameters.

In this paper we limit ourselves to considering an open-loop technique based on spanwise forcing, the streamwise-traveling waves introduced by [1], and explore via Direct Numerical Simulations (DNS) how the drag reduction varies when the friction Reynolds number is increased from Re_τ = 200 to Re_τ = 2000. To achieve high Re while keeping the computational cost affordable, computational domains of reduced size are employed. We adopted special care to interpret results that are indeed still box-size dependent, as well as strategies to compute the random errors and give the results an error bar.

Our results indicate that still R = 0.29 can be obtained at Re_τ = 2000 in the partial region of the parameter space studied. The maximum R is found to decrease as R ˜ Re_τ^−0.22 in the Reynolds range investigated. As most important outcome, we find that the sensitivity of R to Re becomes smaller when far from the low-Re optimum parameters: in this region, we suggest R ˜ Re_τ^−0.08. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The drag reducing properties of wall flows under non-sinusoidal oscillations are analyzed in the present work. The dependency of the drag reduction rate, R, and of the power spent to move the walls, P_in, with respect the shape of the wall motion are investigated. This preliminary work highlights a significant role of the oscillation shape for turbulence control suggesting more research efforts in the field with possible repercussions for practical applications. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three-dimensional direct numerical simulations with a finite-difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The possibility of skin-friction drag reduction in channel flows due to surface structures is investigated numerically. In this context, surface structures with a high width to height ratio compared to the typical dimensions of riblets are studied in the laminar as well as in the turbulent flow regime. In general, it is found that a reduction of the flow resistance is possible in both flow regimes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Presented work is the next step after several experimental examinations of vortex generator influence on a flow separation occurring on a model of the NACA 63A421 airfoil with deflected simple flap. In this stage of research the vortices produced by vortex generators (VGs) were studied using Particle Image Velocimetry technique (PIV) and numerical simulations. Vane type VGs with two spacings among VGs pairs in straight channel with turbulent flow were tested. The average velocity flow field, peak of vorticity and circulation decay downstream of VGs were evaluated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

It will be shown how plasma actuator can generate wall-jet-like flow or train of periodical vortices depending on the generator setting. For generation the high-frequency high-voltage AC is used. Low-frequency modulation of the supply voltage is required to generate vortices. Data acquisition will be performed using time-resolved PIV technique. Phase-averaging will be studied from two different perspectives. Firstly, sampling of phases will be ensured using trigger that is contained in the PIV software and, secondly, phase-averaged flow will be computed from two main modes of POD analysis. The generated flow patterns are to be applied for control of a boundary layer. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Introducing spanwise velocity components into the near-wall flow field of a turbulent boundary layer has shown to be an effective mean of influencing the wall shear stress. The underlying physical mechanisms leading to the drag reduction have however not been fully understood. The presented investigation uses sinusoidal transversal travelling surface waves to influence the near-wall turbulence to achieve drag reduction. Two distinct wave configurations are analysed in detail and compared to an unactuated turbulent flat plate boundary layer flow to gain inside into the drag reducing mechanisms. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Non-contact flow control and flow measurements in hot and aggressive metal melts are big challenges in metallurgical applications. Time-of-Flight Lorentz force velocimetry (ToF LFV) is an electromagnetic measurement technique to meet these challenges. Our experimental results demonstrate that this method is well suited to measure flow rate in turbulent liquid metal channel flow without knowledge of both melt and magnetic field properties. Moreover, the measured flow profiles are in very good agreement with predictions of numerical simulations using the commercial program Package FLUENT MHD. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The motion of a conductor in a magnetic field induces eddy currents whose interaction with the field produces Lorentz forces opposing the motion. One can determine the velocity of the conductor from the force on the magnet system since the latter is equal but opposite to the Lorentz force on the conductor. This contactless method is known as Lorentz force velocimetry (LFV). We study an idealized configuration of LFV, i.e. a rotating solid cylinder interacting with a point dipole. The understanding of parameter influences in this setup can be helpful for more realistic configurations. We use a purely kinematic approach appropriate for low magnetic Reynolds numbers. Numerical results for small and large distances between dipole and cylinder have been obtained with the commercial software COMSOL Multiphysics. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Studying the heat exchange of small, slender objects in a surrounding flow, we approximate the impact of extended heat sources by Dirac-distributions (point sources) with appropriate amplitudes in the context of slender-body theory. The proposed model for the source strength functions is deduced from analytical considerations (Green's functions) of the stationary two-dimensional heat equation. Numerical simulations show the L2-approximation quality of the strategy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An explicit construction of the algebraic equations of the covering surfaces with the noncommutative monodromy groups is done by means of the corresponding homogeneous vector boundary Riemann-Hilbert problem solution. The direct applications concern soliton theory and Landau-Lifshitz equation, in particular. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The scalar Oseen equation represents a linearized form of the Navier Stokes equations. We present an explicit potential theory for this equation and solve the exterior Dirichlet and interior Neumann boundary value problems via a boundary integral equations method in spaces of continuous functions on a C²-boundary, extending the classical approach for the isotropic selfadjoint Laplace operator to the anisotropic non-selfadjoint scalar Oseen operator. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider the fractional step theta time stepping procedure for the non-stationary incompressible linear Stokes equations in a cylindrical domain (0, T) × Ω, where Ω is a bounded domain in ℝⁿ. Using energy estimates and assuming a certain degree of regularity for the data, we show second order L²-convergence. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A maximum modulus estimate for the Stokes system in bounded domains of ℝⁿ (n ≥ 2) is established via methods of hydrodynamical potential theory. The method is based on the unique solvability of the boundary integral equations' system resulting from the double layer potential ansatz together with a projection onto the normal field on the boundary. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In our paper we investigated the initial-boundary value problem for elastic layer situated on half space of another elastic medium. In this medium the thermomechanical interactions were taken into consideration. The system of equations with initial-boundary conditions describes the phenomenon of wave propagation with finite speed. In our problem there are two surfaces ie. free surface and contact surface between layer and half space. On the free surface are setting boundary conditions for normal and tangent surface force. We consider two types of contact between layer and half-space: rigid contact and slip contact. The initial-boundary value problem was solved by using integral transformations and Cagniard-de Hoope methods. From the solution of this problem follows that in layer and half space exist some kind of thermoelastic waves. We investigated moreover the conditions which should be fullfiled for propagation of Rayleigh and Love's type waves on the contact surface between layers and half space. The results obtained in our investigation were used in technical applications especially engineering design and diagnostics of roads and airfields. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution reports on a model describing the evolution of brittle delamination between two visco-elastic bodies Ω₊ and Ω₋, bonded along a prescribed contact surface Γ_C, over a fixed time interval (0, T); a detailed discussion and a rigorous mathematical analysis can be found in [1]. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this note we provide a kind of generalization of the well-known notion of internally (externally, resp.) created oscillations of minimizers of non-convex integrands in the calculus of variations. As an example, we consider a class of 1-dimensional Ginzburg-Landau functionals (the simplest case being considered in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761–825 (2001)). We describe asymptotic behavior leading to multiple small scale separation as parameter epsilon tends to zero. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider the relativistic Euler equations in isentropic fluids with the equation of state , which is the ultra-relativistic limit. We analyze the single shocks. We study the shock interaction, and give explicit example for the non-backward uniqueness. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The presented work deals with an analytical solution for a roll coater with deformable rolls, as commenly used in industry. The focus is on the calculation of the nip feed system in a forward coating mode. The calculation is done with thin film theory and includes Hook's law for elasticity for modelling the elasticity behaviour of the deformable roll. The new model has been validated by experimental data from literature. The agreement is sufficiently good. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)