In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(𝒯_H,P). The resulting ‘coarse’ numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(𝒯_h,p); thereby, only a linear system of equations is solved on the richer space V(𝒯_h,p). Numerical experiments confirming the theoretical results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper presents mixed finite element methods of higher-order for an idealized frictional contact problem in linear elasticity. The approach relies on a saddle point formulation where the frictional contact condition is captured by a Lagrange multiplier. The convergence of the mixed scheme is proven and some a priori estimates for the h- and p-method are derived. Furthermore, a posteriori error estimates are presented which rely on the estimation of the discretization error of an auxiliary problem and some further terms capturing the error in the friction and complementary conditions. Numerical results confirm the applicability of the a posteriori error estimates within h- and hp-adaptive schemes. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Suitable continuous Sobolev embeddings are applied in order to derive smoothness estimators for adaptive hp-refinements in the context of hp-finite element methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present a heuristic for the automated pole selection when the function to be approximated is of Markov type, such as the matrix square root. The performance of this approach is demonstrated at several numerical examples. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. Reliable and easy-to-use a-posteriori error bounds are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and homogeneous fluid layers. In the present investigations, we treat droplets, spreading on rotating solid substrates. Micro-scale effects appear, firstly, at the wetting front, where the film height tends to zero. Secondly, micro-scale effects may appear at other locations, where the free liquid/gas-interface approaches the solid substrate, as e.g. at film rupture. For such situations, molecular effects need to be considered, e.g. in form of the disjoining pressure (DJP), to get physically-correct solutions. Otherwise, the spreading can be modeled within the frame of continuum mechanics, augmented by the (empirical) law of Tanner to capture the contact-line dynamics.

We present, on the one hand, an overview of several interesting issues, as (i) spreading with and without considering the DJP, (ii) spreading after central rupture, including hysteresis effects, and (iii) non-isothermal spreading, including temperature-dependent surface tension (Marangoni effect) and temperature-dependent density (Rayleigh-Bénard effect). On the other hand, we present results for the instability of the contact line, for which the contact line gets corrugated (under isothermal conditions). This instability goes along with a transition from (rotationally-symmetric) two-dimensional to three-dimensional behavior. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The concept of head loss coefficients K for the determination of losses in conduit components is discussed in detail. While so far it has mainly been applied to fully turbulent flows it is extended here to also cover the laminar flow regime which is relevant for micro systems due to the low Reynolds numbers of these flows. Specific numbers of K can be determined by integration of the entropy generation field (second law analysis) obtained from a numerical simulation. It will be shown that a definition of K based on entropy generation is superior to a widely used definition that refers to a pressure drop caused by the conduit component. With the second law analysis details of the physics become available. For example it can be shown that often the main part of the entropy generation occurs downstream of the component. This aspect becomes important when several conduit components are combined in close proximity, like two 90 degree bends that are close to each other. Often in such situations the combination as a whole has to be looked upon as one new complex component. The general approach is discussed and illustrated for various conduit components and combinations of them. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A biological tissue in general is formed by cells, extracellular matrix (ECM) and fluids. Consequently, its overall material behaviour results from its components and their interaction among each other. Furthermore, in case of living tissues, the material properties do not remain constant but naturally change due to adaptation processes or diseases.

In the context of the Theory of Porous Media (TPM), a continuum-mechanical model is introduced to describe the complex fluid-structure interaction in biological tissue on a macroscopic scale. The tissue is treated as an aggregate of two immiscible constituents, where the cells and the ECM are summarised to a solid phase, whereas the fluid phase represents the extracellular and interstitial liquids as well as necrotic debris and cell or matrix precursors in solution.

The growth and remodelling processes are described by a distinct mass exchange between the fluid and solid phase, which also results in a change of the constituent material behaviour. To furthermore guarantee the compliance with the entropy principle, the growth energy is introduced as an additional quantity. It measures the average of chemical energy available for cell metabolism, and thus, controls the growth and remodelling processes.

To set an example, the presented model is applied for the simulation of the early stages of avascular tumour growth in the framework of the finite element method (FEM). (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The importance of lightweight constructions are steady increasing since they promise a low energy consumption together with higher movement speeds. However these demand modern, model-based feed-forward control designs. Especially the undesired vibrations due to the reduced overall stiffness of such manipulators have to be taken into account. A convenient way to model the dynamical behavior of systems that perform large, nonlinear motions superposed with small, elastic deformations is the floating frame of reference approach in a flexible multibody system. The application of the Newton-Euler-Formalism together with D'Alembert's principle to parallel manipulators results in a set of differential-algebraic equations. Therefore, the consideration of the trajectory tracking problem with so-called servo constraints appears to be promising. In case of a non-flat system, the arising set of differential-algebraic equations, which consists of the system dynamics, the holonomic loop closing constraint equations and the servo constraints embodies nontrivial dynamics. With an oblique projection, the embedded set of ordinary differential equations describing the internal dynamics can be obtained. The stability properties of these dynamics determines the complexity of the feed-forward control design, as two-point boundary value problems might have to be solved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The coupling of multibody system dynamics and optical simulations by using ray tracing through moving lens systems will be summarized for both rigid and flexible lens systems. Furthermore, a method will be introduced for efficient simulations in the time domain. This method provides a direct integration of the optical simulation into the equations of motion of a multibody system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Time-optimal motion planning along specified paths is a well-understood problem in robotics for which well-established methods exist for some standard effects, such as actuator force limits, maximal path velocity, or sliding friction. This paper describes an extension of the classical method that allows for considering, on the one hand side, additional non linear constraints such as sticking friction, acceleration limits at the end-effector, as well power limits for the overall system, and on the other, general paths featuring smooth interpolation of angular acceleration as well as arbitrary multibody systems comprising multiple loops. The methods are illustrated with two applications from robotics and the mining industry. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper reviews the singular perturbation control theory in the context of flexible multibody systems. The theory is motivated and explained by a simple, but sufficiently complex model. It is explained that based on the singular perturbed model an end-effector trajectory tracking can be achieved by an integral manifold controller. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The articulated robot ElRob, consisting of flexible links and joints, is considered in several publications. Recent developments are presented in this work.

The overall goal of the research is to decrease the effects of structural elasticities in lightweight robots. For this purpose model-based control concepts are investigated and very accurate and efficient kinematic and dynamic models are necessary. The robot is split into groups of bodies, the so called subsystems, with separated describing velocities and coordinate systems. To obtain structured equations of motion the Projection Equation is used. The beams are modelled using the floating frame of reference formulation and a Ritz-approach.

Because of its flexibility, the examined robot is an underactuated system leading to special difficulties. As an example is it not possible to compute the desired joint angles with respect to a reference path in task space for the flexible system (inverse kinematic problem).

Different methods to solve this drawback and other problems resulting from flexibility are discussed with special focus on feed forward control and different feedback control concepts. The resulting end point error, the necessary control input and other interesting results for the laboratory experiment are presented and compared. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Passively compliant drive concepts are often used in bio-inspired robot designs. Especially fluidic artificial muscles share many characteristics with their natural counterparts. Industrial manipulators can benefit from the increased robustness and safety (in contrast to rigid drives) especially in cooperative human/robot environments. We compare different model-based control concepts for a single rotational joint actuated by two fluidic muscles in combination with proportional valves. While the complete valve and muscle models are already included in this setup, the mechanical model becomes more complex when we extend the control to a full seven axes articulated robot arm with both, electrically and pneumatically actuated joints. In this case the Projection Equation in subsystem description is used for the multibody model, allowing a straight-forward realtime application to different robot kinematics. Remaining model errors and disturbances are handled by observer algorithms. We present measurement results and compare them to simulation outputs. Besides the position control, possible approaches for sensorless external force estimation are discussed. They take advantage of the compliance of the robot and are again based on the actuator and multibody models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work discusses two different structure preserving integrators in the framework of optimal control simulations with contact. The first one is a variational integrator, based on the constrained version of the Lagrange-D'Alembert. The resulting scheme preserves the symplecticity and the momentum maps of the simulated multibody dynamics. The second integrator is an energy momentum scheme and it is based on the augmented Hamiltonian equations, which are discretised using the discrete derivative in [2]. Both integrators are applied to simulate the optimal control of compass gait, for which the contact between the foot and the ground is modelled as perfectly plastic contact. The second example represents a monopedal jumper and it is used to examine the dynamical behaviour of the perfectly elastic and perfectly plastic contact formulation. The resulting differential algebraic equations (DAEs) are solved by the aforementioned symplectic momentum method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mechanical systems with dynamics on varying time scales, in particular those including highly oscillatory motion, impose challenging questions for numerical integration schemes. Tiny step sizes are required to guarantee a stable integration of the fast frequencies. However, for the simulation of the slow dynamics, integration with a larger time step is accurate enough. Small time steps increase integration times unnecessarily, especially for costly function evaluations. For systems comprising fast and slow dynamics, multirate methods integrate the slow part of the system with a relatively large step size while the fast part is integrated with a small time step. Main challenges are the identification of fast and slow parts (e.g. by separating the energy or by distinguishing sets of variables), the synchronisation of their dynamics and in particular the treatment of mixed parts that often appear when fast and slow dynamics are coupled by constraints. In this contribution, a multirate integrator is derived in closed form via a discrete variational principle on a time grid consisting of macro and micro time nodes. Variational integrators (based on a discrete version of Hamilton's principle) lead to symplectic and momentum preserving integration schemes that also exhibit good energy behavior. The resulting multirate variational integrator has the same preservation properties. An example demonstrates the performance of the multirate integrator for constrained multibody dynamics. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Detailed dynamical modeling is the basis for simulation and model based control. In this contribution the Projection Equation is used for the modeling of a biped walking machine, resulting in the equations of motion which are needed for gait generation and verification of its stability. For biped robots one main issue is the generation of stable trajectories for the center of mass (CoM). Several different approaches based on the Zero Moment Point (ZMP) scheme have been presented in the past. Due to the complex dynamic structure of bipedal robots most of the considered algorithms use a linear inverted pendulum as a simplified model. This results in a decoupling of the ZMP equations in lateral and forward direction, but limits the trajectories to a constant height of the CoM. An extension of the well known LQR theory by future reference values has been proposed. This model based approach seems to perform quite well, but does not allow the consideration of constraints on the position of the ZMP. This limitation is removed by the use of Model Predictive Control (MPC) with inequality constraints. By extending this approach to a time invariant one the restriction to a constant height of the CoM is no longer necessary. Both methods as well as the time invariant approach for variable CoM heights have been evaluated in simulations and will be experimentally verified on a real robot soon. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Synthesis of adequate mathematical description of the main mechanical line of rolling mill are considered. The four-mass model with weightless elastic connections is chosen as mathematical model of dynamic system of the main mechanical line of the rolling mill. The problem was reduced to solution of integral equation of the first kind (to unsteady problem). The methods of obtaining of the steady solutions are suggested. Synthesis of the adequate mathematical descriptions with unitary model of external load are suggested. The metal rolling was executed with using of real experimental measurements as an example. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present paper a three-dimensional beam finite element undergoing large deformations is proposed. Since the definition of the proposed finite element is based on the absolute nodal coordinate formulation (ANCF), no rotational coordinates occur in the formulation. In the current approach, the orientation of the cross section is parameterized by means of slope vectors. Since those are no unit vectors, the cross-section can deform, similar to existing thick beam and shell elements. The nodal displacements and the directional derivatives of the displacements are chosen as nodal coordinates, but in contrast to standard ANCF elements, the proposed formulation is based on the two transversal slope vectors per node only. Different approaches for the virtual work of elastic forces are presented: a continuum mechanics based formulation, as well as a structural mechanics based formulation, which is in accordance with classical nonlinear beam finite elements. Since different interpolation functions as in standard ANCF elements are used, a much better convergence rate (up to order four) can be obtained. Therefore, the present element has high potential for application in geometrically nonlinear problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper deals with the dynamical modeling and control of modular redundant robots. The robots under consideration consist of modular actuators (brushless DC motors with Harmonic Drive gears) connected by rigid links. Different configurations can be designed by rearranging these subsystems. In order to fulfill the requirement for an efficient dynamical modeling, the Projection Equation in subsystem representation is used. The subsystems are connected via the kinematical chain. The Projection Equation offers the possibility to calculate the minimal accelerations recursively, leading to an O(n) computational effectiveness. To validate the proposed method, the model of an articulated robot arm with seven joints is considered. Simulation results are compared to measurements. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In many fields of the multi-body world friction must be taken into account. Friction is usually reduced to a ratio: the coefficient of friction. Newer theories also consider dynamic friction laws. For the use in multi-body models, a stepped complexity and measurably hedged description of the friction is necessary. Therefore, different experimental designs that allow dynamic measurements are discussed. An example friction pair is investigated by measurements and the quality of the results is pointed out. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper aims at creating a mathematical model of a bending oscillation rotor system which enables to execute a dynamical analysis of its vibration including the influence of nonlinear bearing characteristics. More specifically, using the finite element method the model of rotating system supported by four hydrodynamic bearings was created. The basic dynamical analysis of the rotor system was performed and the eigenvalues, eigenvectors and stability conditions were evaluated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method.

In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Underactuation occurs, when only some generalized coordinates have a control input. For end-effector trajectory tracking a combined feed-forward and feedback control is often a suitable approach. Feed-forward control design based on an inverse model for underactuated multibody systems is presented. The starting point is the transformation of the multibody system into a nonlinear input-output normal-form. The inverse model follows from this and consists of chains of differentiators, driven internal dynamics and an algebraic part. Especially when using the end-effector as system output the internal dynamics is often unbounded. In order to obtain a viable feed-forward control, a bounded solution must be determined. For this task the internal dynamics is solved as a nonlinear optimization problem. Thereby, the coordinates of the internal dynamics define the objective function which is minimized. The equation of the internal dynamics must be fulfilled at each point of a discrete time grid. In addition continuity of the solution is achieved by adding as equality constraint an integration formula, e.g. trapezoidal rule. The optimization problem is then solved by a SQP-method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper presents a hybrid model to describe drill string dynamics for deep hole drilling. Generally, a typical rotary drill string has a length of several kilometers, but the diameter is less than half a meter. Due to the large ratio of length to diameter, a drill string is a very flexible system. Consequently, an operating drill string is always affected by axial, torsional and lateral vibrations, which potentially induce serious failures. In order to avoid fatal defects, simulations to forecast vibrations are necessary. The simulation should be capable to exhibit the complex dynamical phenomena, e.g. sick-slip, forward whirl and backward whirl, and interactions between drill string and borehole. Usually, these simulations are very time-consuming. In this work, a hybrid model consisting of lumped masses connected with weightless beam elements representing the drill string is developed. The interaction between the drill string and the borehole is implemented by unilateral constraints to describe the nonlinear contact behavior. It was shown that accuracy and simulating time were improved by this model with respect to classical finite-element models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present work deals with optimal control problems governed by differential-algebraic equations (DAEs). In particular, the control effort, which is necessary for moving a multibody system from one configuration to another, will be minimized. The orientation of the rigid bodies will be described using directors, which facilitates the integration of the equations of motion with an energy-momentum consistent time-stepping scheme [1]. This type of structure-preserving integrators offer outstanding numerical stability and robustness properties in comparison to the often applied generalized coordinates formulation. In the context of optimal control, other kinds of consistent integrators have been applied previously in [2] and [3]. We will test the different formulations with two numerical examples, a 3-link manipulator and a satellite. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The choice of coordinates for the description of multibody dynamics has a strong impact on the form of the equations of motion. In the talk two alternative formulations are compared: (i) joint coordinates along with Euler angles for the orientation of rigid bodies, and (ii) redundant coordinates where the orientation of rigid bodies is described in terms of direction cosines. In the case of multibody systems with tree structure the use of generalized coordinates yields equations of motion in the form of ordinary differential equations. In contrast to that, the choice of redundant coordinates yields differential-algebraic equations. The two alternative formulations are compared and their influence on the numerical time integration is highlighted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Active control of flexible vibrations by distributed piezoelectric actuators and sensors plays an increasing role in engineering, especially in light-weight structures. Exemplarily, in this contribution a rotating beam is studied which can be found in many practical applications, e.g. as robot arms or flexible manipulators in production processes. It has been intensively shown in the literature that it is possible to completely suppress the flexible vibrations by an appropriate distribution of piezoelectric actuation strains. In order to compensate the inertial forces in the considered rotating beam, a complex distribution is obtained, such that a practical realisation would be very extensive. To overcome the problem, a discrete approximation by piezoelectric patches is applied. In order to find an optimal configuration for an experimental setup, and to investigate several control strategies, a numerical simulation model has been implemented based on Bernoulli-Euler beam theory. The numerical results are verified by an experimental set-up, in which 48 piezoelectric patches have been attached on a beam with rectangular hollow cross-section. Each patch can be used either as an actuator or a sensor. Additionally, strain gauges can be used as sensors. For monitoring, acceleration sensors are used. The control system is implemented within a dSpace environment. The results show a significant reduction of the flexible vibrations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The paper contains the identification and the taking into account the vibrations produced by the machines, the lathe with different number of rotation, and them action over the human bodies inside the working space. For the identification of vibrations is applied a new method, the Moiré projection method, that did not used until this moment regarding the vibrations action over the human body. Our research was to apply the Moiré projection method to the human hand. They were compared with the measured vibrations using a classic vibrometer with three-axial accelerometer. The results in the booth situation 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. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mechanical stimuli play a crucial role in the differentiation process of mesenchymal stem cells (MSC). The resulting mechanical signals are important in the regulation of various cell functions and maintenance of many tissues. The underlying molecular and biophysical mechanisms of the differentiation process are poorly understood. Present remodelling and growth models are purely phenomenological without linkage to cell mechanisms.

The presented macroscopic model of MSC mechanics is based on a multiphasic-multicomponent formulation within the framework of Theory of Porous Media (TPM), where a single cell is considered as a mixture of interacting constituents. In particular, the constituents are the solid cytoskeleton saturated by a fluid phase (cytoplasm), which itself consists of a liquid solvent and mobile components, e. g., chemical messengers, proteins, etc. To demonstrate the capabilities of the developed model, first qualitative numerical simulations of the impact of external forces on MSC are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present work deals with the incorporation of residual stresses existing in circumferential direction of arterial walls. For the consideration of the residual stresses a novel model will be presented. This model is based on the assumption that residual stresses decrease the stress gradients through the thickness of the arterial wall. Since arterial walls exhibit a pronounced material behavior in fiber direction, the radial gradients of the fiber stresses are considered for the definition of the residual stresses. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling cardiac function is an important task to increase the understanding of the physiological response of the heart and to determine how complex structural heart components influence the biomechanical behavior of the heart. In this communication a coupled model of orthotropic ventricular myocardium is presented using fiber and sheet orientations that is matching regionally measured experimental data. This approach generates a more realistic and homogenized stress distribution when compared to a model with a generic fiber and sheet orientation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution a finite element model for the three dimensional investigation of hip joint contact is described. A shell-like interface element with variable thickness is developed for modelling fluid flow in the synovial gap. For this purpose the Taylor-Hood element is extended in order to take a spatial thickness distribution and local thickness changes into account. The interaction between the synovial fluid and the cartilage layers is solved by a staggered iteration using an artificial compressibility method. Cartilage is modelled using the theory of porous media and three dimensional geometries are reconstructed from medical imaging data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution, a constitutive model adopted from the computational plasticity-models of Drucker-Prager and von Mises is presented. This model captures the material behavior of osseointegration and the curing-process of bone cement. With this basic model, both simulations of bone-ingrowth of uncemented implants and simulations of the curing process of bone cement for cemented implants are carried out in a bone-implant interface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of the paper is to investigate the remodeling phenomenon of a cell-seeded material (collagen type-I) due to collagen type-II newly synthesized by the cells. For the experiments, a cell-seeded condensed collagen gel is mechanically stimulated in a bioreactor for four weeks. The remodeled stiffness of the cell-seeded gel is measured by a compression test and is explained with an evolution law. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This article presents the vibration action on the human body found in a tram travel, where made the vibration measurements. Also presented a mathematical model with two degrees of freedom. Finally a comparison was made between the results obtained from measurements and the results of integration. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present contribution is motivated by the desire to compute physiological loads on the intervertebral discs (IVD) of a human lumbar spine during activities like standing, bending and falling. Following this, a mechanical multi-body system (MBS) is utilised to capture the overall mechanical behaviour of a human, whereas an inhomogeneous, anisotropic, multi-phasic finite-element model (FEM) is applied to resolve the resulting field quantities inside an IVD. In order to couple the FEM of the IVD with the numerically diverse MBS, a homogenisation procedure has to be applied such that field quantities can be converted into discrete quantities. In particular, the MBS captures the mechanical behaviour of an IVD using a bushing element, which provides discrete force-displacement and moment-rotation relations.

The goal of this contribution is to present a homogenisation method for the IVD as well as a possibility to include the homogenised results in the MBS without the need for embedded FE computations in the MBS. Instead, certain deformation modes of the IVD are pre-computed and represented using a non-linear constitutive equations. This task becomes even more challenging, as the resulting discrete DOF of a motion segment appear in a coupled fashion due to the structure of the IVD, i. e., a rotation in the sagittal plane triggers a resulting moment and a resulting force. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to optimize mechanical efficiency creating a naturally optimum structure. The current study utilized an advanced structural optimization algorithm, called design space toptimization (DSO), to perform a three-dimensional computational bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The large-scale simulation utilized a 175 µm mesh resolution with over 23.3 million elements. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using radiography. The results qualitatively showed several anisotropic trabecular regions that were comparable to the natural human femur. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as Wolff hypothesized. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Bone tissues are formed by cells, bone matrix and fluids. The bone matrix is a porous structure, which is remodelled by bone-cells. To describe this process, a coupled systems-biological and biomechanical model is presented.

The macroscopic mechanical behaviour of bone is specified by a biphasic model embedded in the Theory of Porous Media, where the solid phase represents cells and bone matrix, and the fluid phase summarises the extracellular fluids and its components. In this context, the bone remodelling process is described on the macro-scale by a distinct mass exchange that also results in a change of the constituents'material properties.

On the micro-scale, the description of the bone remodelling process stems from a systems-biological cell interaction model. Therein, the bone matrix formation and resorption are a result of the stress-regulated activity of cells.

Here, a staggered solutions strategy is presented. Therein, snapshots of the mechanical stress distribution are calculated on the macro-scale by use of the finite element method. The snapshots are locally evaluated on the micro-scale by use of a cell interaction model, which calculates the long term remodelling process. The evaluation results of the micro-scale are then used to update the reference configuration of the mechanical simulation. As an integrative modelling platform scientific workflows and web-service technologies are employed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Biomechanical simulation of human locomotion is commonly done via dynamical simulations of multibody systems. The actuation of the system is thereby often represented via muscle models that create a force depending on muscle length and activation level. We show a comparison of such a simulation using a structure preserving integration framework to MATLAB/Simulink results. The conclusion is that structure preservation is important to represent such systems correctly, in particular concerning energy and angular momentum evolutions. We introduce a method for structure preserving simulation of muscle actuated movements. Additionally we show examples of a simple arm movement including only one muscle as well as a finger movement including up to six muscles as an example for more complex biomechanical systems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The interaction between capillary fluid films and micro-structural rough surfaces is one of the main challenges in studying self-cleaning mechanisms. The surface behavior of the deformable fluid film is governed by the Young-Laplace equation, which is highly non-linear. Therefore, a numerical solution is introduced using the finite element method, based on a continuum mechanical formulation. Surface and line contact at the fluid-structure interface are modeled by enforcing a contact constraint, and a contact angle, respectively. The numerical solution is validated against the analytical solution of a test case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Propulsion at human dolphin swimming is gained by performing an undulatory motion through the hole body. This movement is similar to undulatory fish motion. Special physical properties like stiffness of upper and lower extremity parts are creating significant unsteady vortex structures around the hole swimmer when performing dolphin kick. The characteristic of these structures and their influence at propulsion are not very well investigated yet. The present paper discribes the creation of a realistic model using data scans of a female swimmer. It is updated with her unique dolphin motion to simulated complete swim motion. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The paper presents a study regarding the linear mechanical models corresponding to hand-arm system. These models was simplified unused the joint in wrist, elbow and shoulder. Also, for these mechanical models effectuated the equations system that would integrate, it obtained the solutions (displacements and velocities) finally. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For surgery training and on-line support during surgeries a method is required which is able to reduce simulation time possibly even to realtime. This contribution compares the effectiveness of three model reduction methods, all of which are widely used for linear problems, in the context of nonlinear structural mechanics. Three reduction methods will be extended to nonlinear elasticity including large deformations. The performance of the extended concepts is investigated for a simplified model of a human inferior turbinate in the context of the functional endoscopic sinus surgery. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The interpretation of human knee joint kinematics in terms of displacements is an outcome of the underlying model of the joint and the measurement technique. Measurement errors and noise challenge the development of optimization procedures which, based on a reduction in degrees of freedom, aim for the reproducibility of joint displacements by computational techniques. So far, optimization algorithms have been applied which are based on a kinematic model of the healthy human tibio-femoral joint (TFJ) as a compound hinge with two fixed orthogonal axes. On the other hand, empirical studies find non-orthogonal rotational axes. Therefore, it was the aim of the present study to investigate the implications of a refined kinematic model on the accuracy of computed joint rotation angles. For the purpose of quantitative comparison, kinematic data of a TFJ with two axes intersecting at an arbitrary angle were simulated. The joint rotations were optimized for the assumption of (a) two orthogonal and intersecting axes (model A), and (b) two axes intersecting at an arbitrary angle (model B). Model B recovers the original input data closer in case of low noise level as encountered in invasive measurement techniques. Skin mounted markers tracking involves non-normally distributed noise which is typically larger by on order of magnitude. In this case, model A exhibits a more favorable performance. These observations motivate the search for alternative kinematic descriptions of the TFJ. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In a seated posture into an autovehicle, humans are most sensitive to whole-body vibrations under low-frequency excitation. This research is focused only on the effect of the backrest angle on the biodynamic response functions. In this paper there are present the results of investigations for 10 participants, whose mean body mass was 61.4 kg. For the biodynamic responses of a seated human body subjected to vertical vibrations, three automotive postures was study: without backrest support, with backrest inclined 7° and respectively 15°, by measurement of transmitted vibration in two different situations: with belt and respectively without this. Knowledge of human responses to vibration provides information about the position of backrest support to mitigate vibration transmitted through the body ensuring the health, comfort and performance. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper introduces, for the first time, a methodology to achieve a forward dynamics simulation of the musculoskeletal system using three-dimensional continuum-mechanical skeletal muscle models. This is achieved by coupling one- and three-dimensional skeletal muscle models. The feasibility of this methodology is demonstrated through a forward dynamics simulation of the upper limb involving the biceps and triceps muscle. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Standard methods for predicting the mechanical response of a human femur bone from quantitative computer-tomography (qCT) scans are classically based on the h-version of the finite element method. These methods are often limited in accuracy and efficiency due to the need for segmentation and the slow convergence rate. With the Finite Cell Method (FCM) a high-order fictitious domain method has been developed that overcomes the aforementioned problems and provides accurate results when compared to high-order finite element methods and experimental results. Herein the FCM applied to the analysis of a patient-specific femur is presented. The femur model is determined based on qCT-scans and the elastic response under compression is presented in terms of strains and displacements. The results are compared with a p-FE analysis and validated by results from an in-vitro test of the modeled femur. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membrane. The basic idea consists in adding to the chosen ionic model one ordinary differential equation for the kinetics of the mechanical activation function. A relevant example illustrates the desired properties of the proposed model, such as delayed muscle contraction and correct magnitude of the muscle fibers' shortening. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The paper contains the transmitted vibrations produce by shocks to the human bodies into the working space.There are the methods for measuring the vibration experiments transmitted through the shock of the human body by the foundation of forging hammer. There are the results given by the different sorts of accelerations into to special conditions of work in the working space. They are of the vibrometer adding the three directions accelerometer. In this way can be analyze taking into account the vibrations action over the human bodies under the action of the equipment in the working space produced by shocks. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to create a defined amount of deformation of the cornea (Goldmann tonometer) or by estimating the diameter of the circular contact area of the cornea and flat tonometer of defined load (Maklakov tonometer). The first simplest models of the applanation method for measurement of the IOP were based on approach, in which an eyeball is modelled as a thin-walled spherical liquid-filled soft shell with corneal biomechanical properties. It was usually supposed that these properties were the same for all patients. In this work numerical simulation have been carried out using finite element code ANSYS. The eye shell is modeled as two joint shells (cornea and sclera) with different mechanical properties. The results are obtained for numerous sets of parameters and were compared to clinical data. For statistics the measurements of IOP for both eyes of 120 patients before and one month after refractive surgery are used. All parameter of refractive surgery (depth, the width and the place of ablation - refractive surgery for myopia or hypermetropia) have effect on IOP reading obtained with both Goldmann and Maklakov tonometry. The results obtained by Goldmann tonometer are significantly more sensitive to all parameters of refractive surgery than those found with Maklakov tonometer with load 10 g. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of this research is to represent, within one modelling framework, selected parts of the musculoskeletal system using principles of continuum mechanics, while other parts are modelled using lumped-parameter models and principles of Multi-Body Dynamics. The most challenging part within such a framework will be to properly model the transition from 3D to 1D models for skeletal muscles as many of the skeletal muscles extend beyond the selected part. Hence, this paper focuses on an interface condition for the 3D-1D transition within a skeletal muscle. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the present paper, the aim was to develop a numerical method for optimisation an existing mechanical material model [1] including muscle activation concerning the excitation of skeletal muscles. The modelling idea was a weak and non-monolithic coupling of an electric current expressed by Ohm's law with a hyperelastic muscle model with transversal isotropic characteristics, see [2]. We confirmed the ability of the proposed model by applying on real reconstructed complex muscle geometry. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

On daily activity a human operator is exposed to vibration in working environment. So, the human body will react in different way. The problem is how much from the initial signal will be sent to the other parts of the body and how much that motion will be damped along the studied parts. The vibrations in horizontal plane are some unexpected, so the human operator will not take any position to prevent them. In this condition the horizontal vibrations will have the higher effect possible. In this paper, the shoulder, neck and the head are modeled together like a mechanical system with four degree of freedom. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An essential property of soft biological tissues is the ability to adapt according to respective loading conditions, e.g. by means of fibre reorientation (remodelling). In particular with regard to arterial tissue, an externally unloaded state of the material is generally associated with residual stresses. In this contribution a three-dimensional micro-sphere-based constitutive model for anisotropic soft biological tissue is presented, which includes fibre-reorientation-related remodelling as well as residual stress-effects. As a key aspect of this contribution, time-dependent remodelling effects are incorporated by introducing evolution equations for the integration directions of the micro-sphere scheme, which thereby characterize the material's anisotropic properties. An appropriate remodelling approach for the orthotropic case is discussed, whereas the effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Unfortunately, the human brain is compromised by an amount of brain diseases, such as strokes or cerebral tumours. In this contribution, special attention is paid to the constitutive modelling procedure and the numerical simulation of the so-called convection-enhanced delivery process, where an effective treatment of malignant brain tumours is achieved by bypassing the blood-brain barrier via a direct infusion of therapeutic agents into the extra-vascular space of the brain tissue using implanted catheters. The modelling approach of the complex brain-tissue aggregate proceeds from the Theory of Porous Media including an elastically deformable solid skeleton, provided by the tissue cells and the vascular walls. The tissue is permeated by two liquid phases, the blood and the interstitial fluid. In order to describe a distribution process of the inserted drugs, the interstitial fluid phase is treated as a chemical solution of two components, the liquid solvent and the dissolved therapeutic solute. The inhomogeneous anisotropic nature of the white-matter tracts is considered by spatially varying permeability tensors, obtained by diffusion-weighted magnetic resonance imaging. The strongly coupled solid-liquid transport problem is simultaneously approximated in all primary unknowns using mixed finite elements and solved in a monolithic manner with an implicit time-integration scheme. The numerical investigation is applied to un-bloody numerical studies. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The material behaviour of skeletal muscles can be decomposed into two parts: an active part, describing the contractile mechanisms, and a passive one, characterising the passive components such as the connective tissue. Computational models are used to support the understanding of complex mechanism inside a muscle. In the present work, we focus on the three-dimensional passive tissue behaviour from the experimental as well as modelling point of view. Therefore, quasi-static experiments have been performed on specimens with regular geometry. By using a three-dimensional optical measurement system the shape of the specimens has been reconstructed at different deformation states. On the modelling side a hyperelastic model with transversal isotropic fibre orientation has been used to describe non-linear stress responses. The model has been validated by performing analyses for different fibre orientations. In summary, it figures out that the proposed modelling approach is able to reflect the experimental results in a satisfying manner. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of the presented work is to characterize the mechanical properties of different types of articular cartilage replacement materials. For this propose an elastic-diffusion model is developed to identify the elastic and diffusion properties of the replacement materials. A set of unconfined compression tests were performed with several kinds of implants. By means of finite element simulation integrated with an user-defined material model, the material parameters were identified. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper concerns with the finite element simulation of textile reinforced concrete (TRC) behavior under tension loading by using discrete cracking concept and fracture mechanics approaches. 3D Finite-Element models are formulated on the meso-scale by simulating all the heterogeneous structural components, the matrix, the fibers, and the fracture mechanisms in both fiber-matrix interface, and the discrete cracks of the matrix. The presented numerical simulation in this study allows for better understanding of the stress distribution and the interaction between all damage mechanisms and the corresponding energy dissipations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In fibre reinforced materials, the interface toughness has a significant influence on strength and damage resistance. Especially in discontinuous fibre reinforced composites, where high densities of fibre ends are apparent, it has been shown that additives which improve the interfacial toughness can increase the effective strength of the materials [1]. Due to the fact that interface properties are strongly dependent on the manufacturing process, only experimental techniques providing the possibility to take these influences into account, are promising for an integrated material characterization. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A boundary element method for the transient thermoelastic fracture analysis in isotropic, continuously non-homogeneous and linear elastic functionally graded materials subjected to a thermal shock is presented. The material parameters are assumed to be continuous functions of the Cartesian coordinates. Laplace-domain fundamental solutions of linear coupled thermoelasticity for infinite, isotropic, homogeneous and linear elastic solids are applied to derive the boundary-domain integral equation formulation. The numerical implementation is performed by using a collocation method for the spatial discretization. Numerical results for the dynamic stress intensity factors are presented and discussed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work outlines an approach that combines the advantages of explicit and implicit descriptions of the crack geometry in the context of the extended finite element method (XFEM). The XFEM is typically combined with an implicit description of the crack which is realized by the level-set method. This facilitates the definition of the enrichments in the XFEM. However, the update of the crack geometry during the propagation of a crack is simpler by means of explicit crack descriptions where the crack surface is meshed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion.

The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical simulations of the formation and the characteristic shape of plastic zones at crack tips in rubber-toughened polymers are performed in order to get a better understanding of the underlying micromechanisms. Complementing previous work, the present study focuses on the contribution of distributed crazing. A macroscopic constitutive model therefore has been developed that describes the overall effect of distributed crazing as an anisotropic flow process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Refractory materials, for example ceramic materials, initially contain a multitude of defects such as voids, microcracks, grain boundaries etc. The deformation process and failure mechanisms due to thermal shock at high temperatures above 1000°C are going along with the creation of new micro defects as well as the growth and coalescence of cracks. A material damage model based on the theoretical concept of damage mechanics and the mechanics of microcracks is presented in this paper. Cell models are developed as representative volume elements (RVE) including crack initiation and growth as well as microstructural shielding effects. For simple configurations of the microstructure, the relation between stress, strain and temperature is derived from analytical considerations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. We focus on the extension of a recently developed phase field model for fracture from the quasi-static setting towards the dynamic setting. It is obtained by taking into account inertial terms and associated dynamic integrators. The introduction of a history field, containing a maximum fracture-driving energy, provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of an extremely robust operator split technique. In a subsequent step, the proposed model is extended to three dimensional problems. The dynamic treatment opens the door to the analysis of complex fracture phenomena like multiple crack branching and crack arrest. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Today, the local approach to fracture is widely applied to simulate the failure of specimens. For ductile damage processes the Gurson-Tvergaard-Needleman model is the quasi-standard. In the last time non-local extensions allowed a mesh-size independent simulation of crack growth. However, most publications dealing with this subject focus upon the convergence regarding global quantities such as the load-displacement relation. Minor attention is paid to the fields directly at the crack tip. Correspondingly, the interrelationship between the intrinsic length of the model and relevant microscopic damage processes at the crack tip is only partly established until now. In the present study the crack propagation is simulated for an implicitly gradient enriched GTN-model within a boundary layer in order to overcome influences of the specimen geometry. The different stages of damage evolution are resolved by a fine mesh. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the pioneering work by Griffith, it is assumed that a crack propagates, if this is energetically favorable. However, this original formulation requires a pre-existing initial crack. In order to bypass this deficiency of classical Griffith theory, Francfort and Marigo advocate a global variational criterion, where the total energy is minimized with respect to any admissible displacement field and crack set. Bourdin's regularized approximation of this variational formulation makes use of a continuous scalar field to indicate cracks. Based on this regularization a phase field fracture model is formulated. The crack field is assumed to follow a Ginzburg-Landau type evolution equation, and cracking is addressed as a phase transition problem. The coupled problem of mechanical balance equations and the evolution equation is solved using the finite element method combined with an implicit time integration scheme. The numerical solution naturally yields the crack evolution including crack propagation, kinking, branching and initiation without any additional criteria. In this work we study the driving mechanisms behind the crack evolution in the phase field fracture model and compare to the purely energetic considerations of the underlying variational formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The breathing mechanism of a transversely cracked rotor and its influence on a rotor system that appears due to the shaft weight is studied. This breathing mechanism is based on experimental and simulation result for the crack shape reported in the literature. If the crack depth is small, the crack closure line is a straight line while for larger crack depths the crack closure becomes more curved. For both cases, a method is proposed for the evaluation of the stiffness losses in the cross section that contains the crack. This method is based on a cohesive zone model (CZM) instead of linear elastic fracture mechanics (LEFM) approach, because LEFM is valid only for the fully open crack and cannot be extended to other intermediate situations. As the crack is closed, the stress intensity factor (SIF) will not appear at the boundary between the closed cracked areas and the open cracked areas. The CZM is developed for mode-I plane strain conditions and accounts explicitly for triaxiality of the stress state by using constitutive relations. The proposed model gives more realistic results than models based on LEFM for the stiffness losses of the crack rotor system for a wide range of the crack depth. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

2-D fracture dynamics' problems for elastic bimaterials with cracks located at the bonding interface under the oblique time harmonic wave are considered in the study. The system of boundary integral equations for displacements and tractions is derived from Somigliana identity taking the contact interaction of the opposite crack faces into account. For the numerical solution the collocation method with piecewise constant approximation is used. The numerical results are obtained for various values of the angle of the wave incidence and the wave frequency taking the friction effects into account. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The thermodynamical and variational consistency of cohesive zone models is analyzed in the present contribution. Based on a naive application of the classical Coleman & Noll procedure, it is shown that the second law of thermodynamics is not fulfilled in general. This can even be seen, in case of hyperelastic interfaces. For guaranteeing thermomechanical consistency, additional surface stresses acting at the interface have to be introduced. Based on such findings, a thermomechanically consistent model including dissipative effects is proposed. This model possesses a natural variational structure. More precisely, all state variables can naturally and jointly be computed by minimizing an incrementally defined potential. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2-dimensional analysis of a single crack with a mode-I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub-boundary value problem represented by a finite element at the growing crack tip. The sub-boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

To characterise the randomly distributed strength and fracture toughness of brittle steels, many specimens have to be destroyed. Since the Small Punch Test (SPT) needs only little material, it is a well suited experiment, when only a small volume of material is available. In this study the cleavage fracture of a ferritic steel at low temperature was investigated using the Beremin model. The failure probability is described with a 2-parameter Weibull distribution in terms of the so-called Weibull stress, which is calculated using an elastic-plastic finite element stress analysis. While the transfer of Weibull parameters works well between similar geometries and loading conditions, it works bad in more general cases. Modifications of the Beremin model are necessary to overcome this problem. Recent publications consider a lower threshold value of the Weibull stress, which leads to a lower Weibull modulus and therefore to a stronger volume size effect of strength. The suitability of this approach to transfer cleavage fracture results from SPT to fracture mechanics specimens was investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Delamination of thermally sprayed corrosion protection coatings as a consequence of thermo-mechanical fatigue is investigated. This study focusses on the modelling of interfacial damage initiation and evolution under cyclic loading with the help of a cohesive zone model. The presented model features a slight non-linearity at unloading from the exponential “damage locus” as well as cyclic damage accumulation restricted to (re)loading conditions. Additionally, an endurance limit is introduced indicating the maximum sustainable traction for an infinite number of load cycles. The capability of the model is demonstrated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Nondestructive test methods are important for examination of elastic devices regarding existence, position and size of cracks. In the case of hidden cracks (which do not touch the boundary), a simple visual control is not sufficient. The basic idea of this paper is to examine appropriate boundary measurements under certain loads. We focus on a method presented by ANDRIEUX, BEN ABDA and BUI [1] for isotropic linear elasticity, and generalize the crack plane detection to anisotropic linear elastic material. The main idea is the use of the reciprocity principle in order to connect data from the outer boundary with the unknown crack properties. Some 2D numerical examples demonstrate, that the method is working with simulated data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Delamination models are derived as the limits of models for partial isotropic volume damage via dimension reduction. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, crack formation and the corresponding failure load of bonded lap joints is analyzed. The analysis is based on linear elasticity solutions for bonded lap joints and makes use of the finite fracture mechanics. A hybrid criterion is applied that states the spontaneous formation of a crack of finite size if a stress and an energy criterion are fulfilled simultaneously. The stress distribution of a linear elasticity solution is used for the stress criterion and for the calculation of the incremental energy release rate which is necessary for definition of the energy criterion. The resulting fracture criterion is compared to literature results and shows a good agreement. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Piezoelectric materials offer many possibilities in advanced engineering structures due to their inherent coupling effects between mechanical and electrical fields and are widely applied in smart devices and structures like transducers, actuators and sensors [2]. An important application of piezoelectric materials is related to layered or laminated composites because they can be optimized to satisfy the high-performance requirements according to different in-service conditions. Beside cracks inside homogeneous domains, one of the most dominant failure mechanisms in layered or laminated composites is the interface failure. Interface cracks and interface debonding may be induced by the mismatch of the mechanical, electrical and thermal properties of the material constituents during the manufacturing process and the in-service loading conditions. This paper presents a hypersingular symmetric Galerkin boundary element method (SGBEM) for crack analysis in two-dimensional (2D), layered and linear piezoelectric solids. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A tensorial framework for strain induced ductile damage of plastically deformed metals is developed in terms of both plastic flow theory and continuum damage mechanics. A symmetric second order damage rate tensor is used in order to study various processes with large finite deformations in combination with damage analysis. The definition of this tensor is physically meaningful since its volumetric and deviatoric parts describe the damage increments caused by an increase in the void volume and by a change in the shape of the void, respectively. Such a view on damage kinetics leads to the introduction of two measures for damage assessment which allow predicting not only a risk of macroscopic failure but also the onset of void coalescence. Material functions appearing in the constitutive equations for damage are determined both by own experiments and by known results from literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An analytical model is developed to analyze stresses in functionally graded (FGM) curved bars under pure bending. Both elastic and partially plastic stress states are considered. The modulus of elasticity of the bar material is allowed to vary. While the model is outlined, important findings are mentioned. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The main aim of this work is the introduction of analysis and synthesis of mechatronical systems including mechanical and electrical elements reducing vibrations. In results of synthesis were received structures and parameters of a discrete model meeting the defined requirements concerning the dynamic features of the system, in particular, the frequency spectrum. The approach adopted makes it possible to take actions aiming at the reduction of phenomena resulting in the unwanted operation of machinery or generation of hazardous situations in the machinery environment. Thank to the approach, the above mentioned preventive activities can be conducted as early as during the designing of future functions of the system as well as during the construction of the system in question. In this work is also comparison of these two kind of elements, mechanical and electrical, of reduction of vibrations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work we present methods for the detection of cracks in plate and shell structures. In contrast to most of the common monitoring methods taking advantage of the reflection of surface waves at crack faces, the presented approach is based on the strain measured at different locations on the surface of the structure. This allows both the identification of crack position parameters, such as length, location and angles with respect to a reference coordinate system and the calculation of stress intensity factors (SIF). The solution of the direct problem is performed on the basis of the BFM (body force method) and the method of assembled point dislocations. The inverse problem is solved applying the PSO (particle swarm optimization) algorithm. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The transverse vibrating mechatronic subsystem is considered. Integral parts of this system are: a continuous beam with known boundary conditions and a transducer, extorted by harmonic voltage excitation, to be perfectly bonded to the beam surface. Findings this article are dynamical characteristics of the discussed mechatronic and mechanical system to model them by hypergraphs. Research limitation is that the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered, however for this kind of systems the approach is sufficient. Practical implications of this researches was that global approach is presented, that means in the domain of frequency spectrum analysis. The methods of analysis and obtained results can be base of design and investigation for this type of mechatronic systems. Originality of this paper is that the mechatronic system created from mechanical and electric subsystems with electromechanical bondage has been considered. This approach is different from those considered so far because is it relies on application approximate methods of analysis of mechatronic subsystem and modeling the one by hypergraph [1-7]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel meshfree model based on the standard element-free Galerkin method incorporated moving Kriging interpolation (MK) is developed for free and forced vibration analysis of 2D structures. Instead of employing moving least square approximation (MLS), shape functions here are constructed by the MK method. Due to the satisfaction of the Kronecker delta function, the essential boundary conditions are thus imposed directly as the finite element method and no special techniques are required. Elastodynamic equations are transformed into a standard weak formulation and then discretized into a meshfree time-dependent equation solved by the standard Newmark time integration method. Some numerical examples of stuctural problems in 2D are attempted, and it is found that the method is adequately accurate and stable for dynamic problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper static Green's functions for functionally graded Euler-Bernoulli and Timoshenko beams are presented. All material properties are arbitrary functions along the beam thickness direction. The closed-form solutions of static Green's functions are derived from a fourth-order partial differential equation presented in [2]. In combination with Betti's reciprocal theorem the Green's functions are applied to calculate internal forces and stress analysis of functionally graded beams (FGBs) under static loadings. For symmetrical material properties along the beam thickness direction and symmetric cross-sections, the resulting stress distributions are also symmetric. For unsymmetrical material properties the neutral axis and the center of gravity axis are located at different positions. Free vibrations of functionally graded Timoshenko beams are also analyzed [3]. Analytical solutions of eigenfunctions and eigenfrequencies in closed-forms are obtained based on reference [2]. Alternatively it is also possible to use static Green's functions and Fredholm's integral equations to obtain approximate eigenfunctions and eigenfrequencies by an iterative procedure as shown in [1]. Applying the Sensitivity Analysis with Green's Functions (SAGF) [1] to derive closed-form analytical solutions of functionally graded beams, it is possible to modify the derived static Green's functions and include terms taking cracks into account, which are modeled by translational or rotational springs. Furthermore the SAGF approach in combination with the superposition principle can be used to take stiffness jumps into account and to extend static Green's functions of simple beams to that of discontinuous beams by adding new supports. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper stabilized mixed triangular finite elements are presented in order to avoid volume locking and to damp stress oscillations. Geometrically non-linear elastic problems are addressed. The mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases. As a key idea, volume and area bubble functions are used for the method of incompatible modes and the enhanced strain method [1], thus giving both the interpretation of a mixed finite element method with stabilization terms. Concerning non-linear problems these are non-linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used [1]. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two-field method, the method of incompatible modes and the enhanced strain method in finite deformation problems is derived for a hyper elastic Neo-Hookean material. In the representative example Cook's membrane problem illustrates the good performance of the presented approaches compared to existing finite element formulations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The scaled boundary finite element method (SBFEM) is extended to the static analysis of thin plates in the framework of Kirchhoff's plate theory. The governing equations are transformed into scaled boundary coordinates. Applying a discrete form of the Kantorovich reduction method results in a set of ordinary differential equations, which can be solved in a closed-form analytical manner. The element stiffness matrices for bounded and unbounded media can be computed, using appropriate subsets of the analytical solution. Examples show the efficiency of the method, applied to plate bending problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The contact situation between the brake pad and the disc during the braking process is of particular importance concerning the squeal behavior of brake systems. After the braking process, the surface topography of brake pads can be measured using a confocal microscope. An algorithm to calculate the contact between two surfaces has been developed at the Institute of Dynamics and Vibrations. The algorithm calculates the deflection of asperities under a normal load regarding an elastic material behavior. A normal load is applied to a measured surface topography of the brake pad; the counter body (brake disc) is represented by a flat surface. The potential contact area, the locally distributed forces, deflections and normal stiffness of the pad are computed. Since there is an uncertainty in the relative position between the pad and the disc and hence the real contact situation during the braking process is not known, different contact situations must be considered during the simulations. Concerning various tilt angles of the pad that can arise during the vibrations of the brake system, a sensitivity study has been carried out. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Isogeometric analysis is a high-continuity alternative to the standard finite element method. However, for practical application several issues remain to be addressed. This contribution discusses the imposition of Dirichlet boundary conditions as well as the connection between multiple patches. In particular necessary manipulations of the geometrical input data are provided. Dirichlet boundary conditions can be imposed in weak or in strong form. Due to the non-interpolatory characteristics of NURBS surfaces weak imposition of Dirichlet conditions is a viable option which avoids local transformations. The connection of multiple patches can be realized in a weak manner by adding additional terms to the variational equations, for example by the Lagrange multiplier method or the perturbed Lagrangian method. Both base on the idea of multiplying the mutual deformations with an additional unknown to force the deformations on shared edges to be equal. The numerical treatment leads to different sets of equations. In contrast to strong inter-patch connections, where coinciding control points share the same degrees of freedom, weak imposition allows for hanging nodes and therefore local refinement. The theoretical background and issues of implementation are given. Some numerical examples compare error norms for all mentioned methods and demonstrate that in particular cases a reduction of continuity leads to more accurate results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present work aims to investigate stable time integrators for large deformation contact problems within the framework of the well known node-to-segment (NTS)-method. For this kind of problem, standard time integrators fail to conserve the total energy of the system. To remedy this drawback, we combine a mixed method with the concept of a discrete gradient applied to the aforementioned NTS-method. In the context of nonlinear elastodynamics stable integrators for ordinary differential equations have been extensively developed and investigated during the last two decades. For contact problems, energy consistent integrators have been developed for the NTS-method (see e.g. Ref. [1]). (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A new soft computing approach is described, which can be applied for the identification of uncertain time-dependent material behaviour. Artificial neural networks are utilized for model-free material formulations. Uncertain stress-strain-time dependencies obtained from uncertain results of experimental investigations are described by recurrent neural networks for fuzzy data. An incremental finite element formulation is presented using neural networks instead of material models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, new solid-shell and solid-beam finite element formulations for finite deformation problems are introduced. One application of interest, concerning these types of elements, can be found in the simulation of stent implementation in the treatment of stenosis. The beam-like structure of the stent and the shell-like structure of the blood vessel can be modelled easily by using these types of elements. Moreover, the modelling of the interaction of the different structural types between each other and with the surounding tissue becomes more simple. A high rate of convergence, by using only one element in thickness direction that is comparable to classical structural elements, can be named as a major requirement for the element formulations. In this regard, different locking effects are cured by a special combination of the assumed natural strain method (ANS) and the enhanced assumed strain method (EAS). In addition a variable number of quadrature points can be used in thickness direction in order to capture nonlinearites. This is combined with the concept of reduced integration for the sake of computational efficiency. An adaptive hourglass stabilization that also accounts for material nonlinearities is a crucial issue in this regard. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper a new approach for designing mechatronic vibrating branched structures has been presented. Mechatronic structures have been built from mechanical discrete systems connected to piezoelectric actuator and externalL_xR_xC_x network, with different configurations. Modeling simplification has been performed by use of non dimensional transformations and retransformations. In each case reverse task has been solved by distribution into partial fraction method in respect to required dynamic properties in form of frequency spectrum: resonant and anti resonant frequencies. Furthermore, different configurations of final L_xR_xC_x network have been presented. These considerations have been supported by calculation examples, and all results have been presented in the graphical form. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We will present a comparison between two formulations of the normal vector field for contact algorithms based on the mortar method. First the non steady normal field is discussed. The non steadiness is a result of the C⁰ continuity of the boundary discretization. This is the common result if one discretize the domain with classical finite element methods. Second we will present results for a special normal field distribution. We average the nodal normal vector of two ascending edges and interpolate this nodal normal throughout the edges. We have implemented both methods and present comparisons based on numerical experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Due to the roughness of technical surfaces only the surface peaks are in contact for moderate contact pressures. Thus, the real contact area is smaller than the apparent contact area. Contact forces can only occur in the real contact area. Consequently it is necessary to determine the deformation of surface asperities in order to analyse the tribological properties of surfaces. The real contact area is usually small in initial contact. This leads to large contact pressures which in turn lead to the plastic deformation of surface roughness peaks. Therefore an elastic-plastic model is necessary. The halfspace model seems to be beneficial because there is only a system of equations on a surface mesh to be solved and not on a volume mesh like in the Finite-Element-Method. This leads to a much smaller system of equations which should allow reasonable calculation times even for large contact surfaces. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, a molecular mechanics model embedded in the finite element framework is applied to analyze the buckling behaviour of carbon nanotubes. Within this model a specific finite element is set up for the underlaying interatomic potential describing the behaviour of the multi particle system. The model relies on the fully nonlinear description of the interatomic potential and the atomic kinematics. Stability points of the system are located by an accompanying eigenvalue analysis and the bifurcation point is detected using a bisection algorithm. To follow the nonlinear load-deformation path in the area of postbuckling a branch switch is performed. With the help of this molecular mechanics model, the response of carbon nanotubes on different loading conditions with respect to buckling is studied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Simply supported rectangular Kirchhoff-plates with two-parametric Pasternak-type foundation are studied under the action of a transient temperature moment, which is span-wise constant. In extension to a previous study it can be shown, that an excellent convergence of the series solutions of the static problem can be achieved by means of Kummer's transformation and Cesaro's generalized C₁-Summation. The convergence improvement of the other types of the solutions can be performed analogously. The dynamic solution for the deflection and shear forces is computed using the derived efficient solution for the quasi-static case with fast convergent Fourier series. Modal expansion is applied for the computation of the vibrations about this quasi-static part. The results of he analytical solution for defined parameters of the foundation are shown for some characteristic points of the plate and compared to the FE computation results . (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A beam held by two spatially fixed supports, may slide relative to these as soon as external loads are imposed. In particular, the possibly large deformation of a shear-deformable beam under a uniformly distributed, transverse force is investigated, which is clamped at its left side, while it may slide horizontally through another clamping device at its right side. Consequently, the material point of the beam that is currently located at the latter and the length of the portion of the reference configuration situated in between the two supports depend on the external forces and therefore are not known in advance. In order to obtain approximate solutions, a finite element scheme is utilized, in which a coordinate transformation is introduced, by which the difficulties of non-material boundary conditions and the unknown length of the beam are circumvented elegantly. It turns out that no static equilibrium is found, if the external forces are increased beyond a critical value, since the beam would slide out infinitely in that case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper proposes an identification method for general linear time-varying (LTV) MDOF systems and weakly nonlinear systems based on the Hilbert-Huang Transform (HHT)[1]. The proposed method uses Empirical mode decomposition (EMD) to decompose the response signals of systems into intrinsic mode functions (IMFs) and residues, and then analyzes the IMFs and the residues by Hilbert transform (HT) to obtain the analytical IMFs and analytical residues. After that, the above signals are synthesized to form new response signals and new analytical response signals. Finally, the new synthesized signals are used to identify the stiffness and damping coefficients of the systems. Three types of variation: smooth, abrupt and periodical variations are considered in the numerical simulations of LTV chainlike[2] and nonchainlike systems as well as weakly nonlinear systems such as Duffing oscillators and Van der Pol oscillators with white noise added in the system responses to demonstrate the effectiveness, accuracy and robustness of the proposed method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

A finite element formulation of a reduction method for dynamic stability analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The single mode dynamic buckling analysis and its extension to parametric excitation analysis are described. The approach is available within a general purpose finite element code. Characteristic results for the parametric excitation analysis of a composite cylindrical shell are shown. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The numerical simulation of timber structures by means of FEM has been an object of recent research. Most of the material models developed so far are based on idealized assumptions by disregarding inhomogeneities. Here, models to capture structural inhomogeneities in terms of branches and knots and the resulting deviation in grain course in a three-dimensional FE analysis are presented. Besides, naturally varying material properties referred to as material inhomogeneities have to be considered in the structural analysis. Due to the insufficient experimental data, the uncertainty model fuzziness is applied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The process integrated powder coating by radial axial rolling of rings represents a new hybrid production technique in order to apply the functional layers on ring-shaped work pieces. Since the layer is produced in a powder metallurgical way [1], the ring volume decreases during the compaction of the layer material. In conventional ring rolling processes an isochoric plastic deformation of the ring is exploited in order to control the process. However this is not true any more for a ring exhibiting a compressible layer [2]. Consequently different control mechanisms have to be developed for the new considered process. One major aspect is the stability of the process which is governed by a stable position of the ring as well as the roundness of the ring. Therefore the finite element (FE) model has been coupled with a PID-controller unit and it will be shown that a stable process can be reached in this way. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The kinematics and kinetics of a compliant mechanism are analyzed quasi-statically. The mechanism consists of a parallelkinematic (Biglide type) with the particular feature, that its revolute joints are implemented by flexure hinges. In the considered example the flexure hinges are uniform beams similar to leaf springs. The preliminary considerations with a rigid body system and by linear theory of elasticity result in an initial geometry. In order to predict the large displacement behavior more precisely the theory of Elastica is used. An optimization method is applied to solve the mechanism's state of deformation. It was found that some aspects can be approximated by a pseudo rigid body system, while others, namely the rotation, cannot be rendered. The decreased stiffness in the highly deformed operating state appears as key problem. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The problem of the interaction of a finite number of holes in an elastic plane or half-plane is considered. The analysis is based on the complex potential method of Muskhelishvili as well as on the theory of compound asymptotic expansions by Maz'ya. An asymptotic expansion of the complex potentials in terms of relative hole radii is constructed. This expansion is uniformly valid in the whole domain. The method leads to a simple procedure which does not involve any coupled system of linear equations. The successive closed-form approximations can be obtained in an iterative manner to an arbitrary order without any need for numerical approximation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The main goal of the present work is to develop two structure-preserving time integrators, which are based on the works of Öttinger [1] (GENERIC formalism), Romero [2] (Thermodynamically consistent (TC) algorithm) and Groß [3] (enhanced hybrid Galerkin (ehG) method) and compare them with standard integrators considering a thermoviscoelastic double pendulum. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

During the production of high-grade wooden components often the conditioning with coated abrasives composes the end of the process train. The chipping process and the resulting wood surface are depending of the scatter pattern parameters (particle size and distribution, …) and their time depending variations. Till now, no models exist concerning the interaction of the scatter pattern with the grinding process, the work piece surface and the clogging. The developed model is based on cooperating cellular automata. One is describing the sandpaper, the other one the work piece. These two automata interacts witch each other. Update rules are designed by physical laws and measurements. The paper shows surprising results with respect of surface structures which are the result of self-organization effects in the boundary layer of wood and sandpaper. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Boundary Element Method is quite suitable for solving dynamic semi-infinite or infinite linear problems. In order to establish the boundary integral equations, one crucial condition is the knowledge of corresponding fundamental solutions. For a partially saturated poroelastic continuum, the governing equations in Laplace domain are formulated based on the theory of mixtures, and the related fundamental solutions are derived by using Hörmanders method. The singular behavior of the fundamental solutions are investigated by a series expansion with respect to the variable r. Finally, some exemplary fundamental solutions are calculated to visualize the principal behavior as well, and comparisons with the related results of saturated poroelasticity are given. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Das Übertragungsverhalten sowie die Eigenfrequenzen und Eigenformen zweier Statorblechpakete wurden experimentell und numerisch, mittels einer Modalanalyse eines homogenen Finite-Elemente Modells, ermittelt. Durch geeignete Abstimmung der Materialparameter des Simulationsmodells wurde die Strukturantwort an die der Messung angepasst. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In linear poroelasticity so far only collocation boundary element methods have been available. However, in some applications, e.g., when coupling with finite elements is desired, a symmetric formulation is preferable. Choosing a Galerkin approach which involves the second boundary integral equation, such a formulation is possible. Here, a previously presented integration by part technique for the regularization of the first boundary integral equation is extended to the second boundary integral equation as well. While the weakly singular representation of the double layer operator has been presented before, the emphasis lies here on the so called hyper-singular boundary integral operator. Due to the regularization, this operator can be evaluated numerically and, hence, be used within a numerical scheme for the first time. Different numerical studies will be presented to show the behavior of the established symmetric Galerkin boundary element method, also comparing it with collocation boundary element methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The computation of ropes and cable constructions considering contact as well as friction is often required in engineering practice. That includes mutual frictional contact between two and more ropes and frictional contact between ropes and solid –mostly assumed as rigid– bodies. The latter occurs especially in the mechanical model of a rope wound around a cylinder. So the main topic of this contribution is the development and FE-implementation of a "Segment- To-Analytical-Surface (STAS)"-contact-element which can be used to describe the mechanical model of a rope wound around a cylinder. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Two distinct analytical models are described representing geometrically nonlinear instabilities in layered composites under in-plane compression — kink-banding and delamination buckling. The utilized technique is based on of energy minimization principles in order to examine the underlying mechanics of the systems. It is demonstrated that using this approach enables investigations to be undertaken far into the postbuckling range whilst changing system parameters. Thereby a greater phenomenological understanding of the mechanics of the systems is achieved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The aim of contribution is to formulate a certain extended version of the tolerance modelling technique for functionally graded composites. For the sake of simplicity, the considerations are restricted to the bidirectionally graded heat conductors. It is shown that the proposed approach enables to determine an entire class of mathematical models for which applications can be found in various specific problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In quasistatic solid mechanics the spatial as well as the temporal domain need to be discetized. For the spatial discretization usually elements with linear shape functions are used even though it has been shown that generally the p-version of the finite elemente method yields more effective discretizations, see e.g. [1], [2]. For the temporal discretization diagonal-implicit, see e.g. [4], and especially linear-implicit Runge-Kutta schemes, see e.g. [5], [6], have for smooth problems proven to be superior to the frequently applied Backward-Euler scheme (BE). Thus an approach combining the p-version of the finite element method with linear-implicit Runge-Kutta schemes, so-called Rosenbrock-type methods, is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this article we propose a non-local damage model for dynamic finite element computation of viscoplastic thin-shell structures. To take void nucleation and growth into account, 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. The dynamic thin-shell elastic theory including large rotations proposed by Simo and Tarnow (1994) is used to capture finite deformation. Local constitutive laws considering viscoplastic behaviour, isotropic hardening and isotropic ductile damage leading to softening in Velde et al. (2009) are employed. The performance of the proposed approach is demonstrated through the preliminary numerical simulations of shock-wave loaded structures, which are validated by comparision with the experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For continuous vibrating systems, such as bars and beams, end-mounted in the environment, knowledge about the mass, damping and stiffness properties of the resonating environment is important for analyzing free and forced vibrations of such structural members which are also damped themselves. To finally get an identification of the clamping parameters, examinations of both vibrating structural members for various restraint conditions and dynamic interaction with viscoelastic halfspaces, etc., are required. As a first step, longitudinal bar vibrations are studied in detail. The method of separation of variables combined with the reformatted orthogonality relation, and numerical integration is applied for calculating the free and forced oscillations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Paper presents analysis of an one-dimension flexural vibrating mechatronic system. The considered system is a cantilever beam with a piezoelectric transducer bonded to the beam's surface. An external electric circuit is adjoined to the transducer's clamps in order to damp vibrations. System was analyzed on the basis of an approximate Galerkin method. Verification and assumptions of the approximate method were described in the previous papers where analysis of the mechatronic system with piezoelectric shunt damper was presented. Structural damping of all system's components was being taken into consideration. Rheological properties were introduced using Kelvin-Voigt model of materials. Influences of component's structural damping coefficients values on the system's dynamic flexibility were defined. Obtained results were presented on 3D graphs as dynamic flexibility dependence on the structural damping coefficient and frequency of an external force that was applied to the system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In quasistatic solid mechanics the initial boundary value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements. For the temporal discretization three different classes of Runge-Kutta methods are compared. These methods are diagonally implicit Runge-Kutta schemes (DIRK), linear implicit Runge-Kutta methods (Rosenbrock type methods) and half-explicit Runge-Kutta schemes (HERK). It will be shown that the application of half-explicit or linear-implicit Runge-Kutta methods can enormously reduce the computational time in particular situations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Finite Element Method (FEM) and the Boundary Element Method (BEM) are the most used numerical tools for solid mechanics analysis. Each one of these methods has advantages and drawbacks in different cases. In order to take advantage of both methods, a nonoverlapping domain decomposition method FEM - BEM in elastodynamics is presented. The domain is divided in two subdomains and each one of them is analyzed separately and only the interface information is exchanged. An iterative Neumann - Dirchlet algorithm with relaxation is used, to get continuity and the equilibrium conditions at the interface. The FEM time integration is carried out using the Newmark's method and the BEM approach in time domain is based in the Convolution Quadrature Method developed by Lubich. Numerical examples are presented to show agreement with other available numerical results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The plane problem of a bi- or trimaterial-junction, consisting of dissimilar, homogeneous, isotropic and linear elastic sectors is considered. The asymptotic behaviour of the stresses of this composite situation is analyzed by the complex variable method, based on an appropriate choice of the Kolosov-potentials which are applicable in the vicinity of the vertex. In the analyses, the identification of the singularity exponent is emphasized. With the help of a novel approach it is demonstrated how to derive some solutions for the orders of the stress singularities at bi- and trimaterial combinations in a closed-form analytical manner. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Considering a simply supported plate under uni-axial compression it is well-known that after buckling the stress concentrates at the unloaded boundaries as the out-of-plane displacement at the buckle causes an in-plane relaxation, i.e. a decrease of the mid-plane stress. This stress distortion is described by the so-called effective width. The knowledge of the effective width allows the calculation of the stress at the unloaded boundaries, which is usually considered as the highest stress in the plate. However, the out-of-plane displacement also bends the plate, which produces additional stresses. This article analysis the fundamental question, if the total stress at the surface of the buckle is higher than the stress at the unloaded boundaries. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Finite Cell Method (FCM) combines the fictitious domain approach with high-order finite elements and adaptive integration. For linear elastic problems with smooth solution, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. In this contribution, the FCM idea is combined with standard finite element technology for the solution of geometrically nonlinear problems. In particular, a modified FCM formulation is introduced, which resets the deformed configuration of the fictitious domain to the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis with very small values of the penalty parameter, while the accuracy of the geometrically nonlinear solution within the physical domain remains unaffected. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mathematical homogenization (or averaging) of composite materials, such as fibre laminates, often leads to non-isotropic homogenized (averaged) materials. Especially the upcoming importance of these materials increases the need for accurate mechanical models of non-isotropic shell-like structures. We present a second-order (or: Reissner-type) theory for the elastic deformation of a plate with constant thickness for a homogeneous monotropic material. It is equivalent to Kirchhoff's plate theory as a first-order theory for the special case of isotropy and, furthermore, shear-deformable and equivalent to R. Kienzler's theory as a second-order theory for isotropy, which implies further equivalences to established shear-deformable theories, especially the Reissner-Mindlin theory and Zhilin's plate theory. Details of the derivation of the theory will be published in a forthcoming paper [3]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In lightweight design the webs of beams which are loaded by bending are often provided with holes. Aim of this article is to present a method to calculate the shear strength of webs with certain holes. The semi-analytical method is derived with respect to the results of geometrically and physically non-linear numerical simulations in which the shear strength of the web is calculated. The method consists of a plastic failure approach for rather thick webs and a framework analogy to model the failure of a solid web after onset of buckling. To take the influence of the holes into account the shear strength of the solid web is reduced as a function of geometry parameters. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The effect of free edges of a monoatomic graphene sheet leads to excess edge energy due to the reconstruction of dangling bonds. Molecular static calculations show, that individual carbon atoms near the edge are displaced out of plane for relaxed nanoribbons [1]. In this work we are considering the effect of excess edge energy for almost circular graphene patches. To tackle this problem in the framework of continuum mechanics we are modelling the edge effect with a non-Euclidean plate model. A linear stability analysis of the flat configuration leads to the stability boundary in the parameter plane. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The authors of the present paper outline aspects on the optimization of the a TR-type industrial robot structure movements in order to generate the manipulation space to a flexible manufacturing cell with a parallel organization designed for the pallet and container operation of paint-filled recipients. The paper contains the direct and inverted geometrical modelling of the robot structure using the 3*3 rotation matrix method and the algebra method. After knowing the characteristic point movement of the prehension device, graphics for the variation of the TR robot's general coordinates and for the trajectory of the prehension device's characteristic point of its work space were performed by using the Mathematica 6.0 soft. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Shakedown analysis by using the lower-bound theorem leads to computationally intensive nonlinear convex optimization problems with a large number of unknowns and constraints. Interior-point algorithms such as recently developed by the authors have proven to be efficient for the solution of these problems. For convergence and efficiency of the iterative process of these algorithms the choice of the starting-point is crucial. It should be inside of the feasible region and well-centered for fast convergence.

No general method exists for the construction of optimum starting-points and only few investigations have been published on this issue. In this paper the physical meaning of the involved variables in shakedown problems is used to optimize starting-points. The efficiency of the new method is illustrated by a numerical examples and comparison with an alternative approach. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Two mechanical models for an axially moving beam supported by discrete elastic springs are derived, analysed and compared. It is considered that the beam has a constant thickness, a predefined temperature distribution and a given transversal load. The first beam model applies global Ritz approximations for the spans with springs. Gauss integration points are used in longitudinal and transverse direction. The second beam model uses a conventional FE description. The thermal and pressure loads cause stresses, which lead to strain rates due to creep of the material so that a time dependent deformation between the elastic supports results. Here the axial motion is considered to be so slow so that inertia effects can be neglected. The axial transport of the inelastic creep-strains has been considered in the computation. The temperature field is constant and fixed in space. The deflection of the axially moving beam model is computed considering a variable number of spans separated by elastic springs. The computed results of the two mechanical models are compared for a beam with two spans. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Metal-ceramic composites are widely applied in the different brunches of industry. The composites are produced by squeeze-casting of the ceramic preform by molten aluminum alloy. The lamellar microstructure is obtained during freezing of ceramic suspension. The internal structure of the domains can be controlled via freeze-casting parameters. The material has high anisotropy level and its effective properties depend on lamella orientation. The aim of this study is numerical simulation of the inelastic behavior of the material and its verification by experiment. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

The purpose of this work is the application of the least-squares finite element method to an elastodynamic, quasi-incompressible problem under small strain assumptions. Therefore a mixed finite element based on a weighted least-squares formulation is developed. The L₂-norm minimization of the time-discretized residuals of the given first-order system of partial differential equations leads to a functional depending on displacements and stresses. In the numerical example the proposed mixed element is compared to an alternative approach, which is based on a least-squares mixed finite element with improved momentum balance, see [1]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Optical 3D field measuring systems, based on DIC (Digital Image Correlation) deliver kinematic quantities. They are appropriate devices helping to understand the material behavior especially at high strains. One problem of these systems is the missing information about material points located behind the observed surface of the specimen, which is needed to assign the full deformation gradient. Different ways of dealing with raw point coordinate data that is confidently given by the metrology system lead to different kinematic results. To ensure the correctness of strain-like results determined by the system, they are compared to analytical and finite element calculations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

If circular metal plates are subjected repeatedly to impulsive loadings, damage and failure of the structures can occur. In order to predict the damage evolution in finite element simulations, a structural theory combined with viscoplastic constitutive equations acounting for damage is used. However, different structural hypotheses, used in the theoretical model, can lead to variations in the numerical result. Therefore, first- and third-order shear deformations theories are applied in a finite element code. Moreover, local and non-local damage approaches are used. The aim is to determine the numerical model, which leads to the most accurate results compared to experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

An usual approach to investigate nonlinear systems in the frequency domain is the application of the Harmonic Balance Method (HBM), assum