It is known that the explicit time integration is conditionally stable. The very small time step leads to increase of computational time dramatically. In this paper, a mass-redistributed method is formulated in different numerical schemes to simulate transient quasi-harmonic problems. The essential idea of the mass-redistributed method is to shift the integration points away from the Gauss locations in the computation of mass matrix for achieving a much larger stable time increment in the explicit method. For the first time, it is found that the stability of explicit method in transient quasi-harmonic problems is proportional to the softened effect of discretized model with mass-redistributed method. With adjustment of integration points in the mass matrix, the stability of transient models is improved significantly. Numerical experiments including 1D, 2D and 3D problems with regular and irregular mesh have demonstrated the superior performance of the proposed mass-redistributed method with combination of smoothed finite element method in terms of accuracy as well as stability. This article is protected by copyright. All rights reserved.

A number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method (FEM) and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf-sup (LBB) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and FEM algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so-called *up* and *uvp* formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes. This article is protected by copyright. All rights reserved.

When using particle methods to simulate water-air flows with compressible air pockets, a major challenge is to deal with the large differences in physical properties (e.g. density and viscosity) between water and air. In addition, the accurate modelling of air compressibility is essential. To this end, a new two-phase strategy is proposed to simulate incompressible and compressible fluids simultaneously without iterations between the solvers for incompressible and compressible flows. Water is modeled by the recently developed 2-phase Consistent Particle Method (2P-CPM) for incompressible flows. For air modeling, a new compressible solver is proposed based on the ideal gas law and thermodynamics. The formulation avoids the problem of determining the actual sound speed which is dependent on the temperature and is therefore not necessarily constant. In addition, the compressible air solver is seamlessly integrated with the incompressible solver 2P-CPM because they both use the same predictor-corrector scheme to solve the governing equations. The performance of the proposed method is demonstrated by three benchmark problems as well as an experimental study of sloshing impact with entrapped air pockets in an oscillating tank. This article is protected by copyright. All rights reserved.

In this article, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three-dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have superconvergence in the *l*_{2} norm at nodes of a CVDT mesh for an arbitrary three-dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method. Copyright © 2016 John Wiley & Sons, Ltd.

A new boundary element formulation is developed to analyze two-dimensional size-dependent piezoelectricity response in isotropic dielectric materials. The model is based on the recently developed consistent couple stress theory, in which the couple-stress tensor is skew-symmetric. For isotropic materials, there is no classical piezoelectricity, and the size-dependent piezoelectricity or flexoelectricity effect is solely the result of coupling of polarization to the skew-symmetric mean curvature tensor. As a result, the size-dependent effect is specified by one characteristic length scale parameter *l*, and the electromechanical effect is specified by one flexoelectric coefficient *f*. Interestingly, in this size-dependent multi-physics model, the governing equations are decoupled. However, the problem is coupled, because of the existence of a flexoelectric effect in the boundary couple-traction and normal electric displacement. We discuss the boundary integral formulation and numerical implementation of this size-dependent piezoelectric boundary element method (BEM), which provides a boundary-only formulation involving displacements, rotations, force-tractions, couple-tractions, electric potential and normal electric displacement as primary variables. Afterwards, we apply the resulting BEM formulation to several computational problems to confirm the validity of the numerical implementation and to explore the physics of the flexoelectric coupling. This article is protected by copyright. All rights reserved.

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. The performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general the Cartesian parametrization is more robust and more numerically efficient than the others. Copyright © 2016 John Wiley & Sons, Ltd.

This manuscript presents the formulation and application of the Green's Discrete Transformation Method (GDTM) for the meshfree simulation of transient diffusion problems, including those with moving boundaries. The GDTM implements a linear combination of time-dependent Green's basis functions defined on a set of source points to approximate the field in the form of a solution series. A discrete transformation is implemented to evaluate unknown coefficients of this series, which eliminates the need to use time integration schemes. We will study the optimal number and location of the GDTM source points that yield the highest level of accuracy, while maintaining a manageable condition number for the resulting linear system of equations. The optimal values of these parameters, which are inherently independent of the domain geometry, are determined such that the basis functions have appropriate features for approximating the field. A comprehensive convergence study is presented to show the precision and convergence rate of the GDTM for modeling various diffusion problems. We also demonstrate the application of this method for simulating three diffusion problems with complex and evolving morphologies: heat transfer in a turbine blade, thermal response of a porous material, and localized (pitting) corrosion in stainless steel. This article is protected by copyright. All rights reserved.

This paper presents a method which applies pseudospectral tau approximation for retarded functional differential equations (RFDEs). The goal is to construct a system of ordinary differential equations (ODEs), which provides a finite dimensional approximation of the original RFDE. The method can be used to determine approximate stability diagrams for RFDEs. Thorough numerical case studies show that the rightmost characteristic roots of the ODE approximation converge to the rightmost characteristic roots of the original RFDE. Application of the method to time-periodic RFDEs is also demonstrated, and the convergence of the stability boundaries is verified numerically. The method is compared with recently developed highly efficient numerical methods: the pseudospectral collocation (also called Chebyshev spectral continuous-time approximation), the spectral Legendre tau method and the spectral element method. The comparison is based on the stability analysis of three linear autonomous RFDEs. The efficiency of the methods is measured by the convergence rate of stability boundaries in the space of system parameters, by the convergence rate of the rightmost characteristic exponent and by the computation time of the stability charts. Copyright © 2016 John Wiley & Sons, Ltd.

Smoothed molecular dynamics (SMD) method is a recently-proposed efficient molecular simulation method by introducing one set of background mesh and mapping process into molecular dynamics (MD) flow chart. SMD can sharply enlarge MD time step size while maintaining global accuracy. MD-SMD coupling method was proposed to improve the capability to describe local atom disorders. The coupling method is greatly improved in this paper in two essential aspects. Firstly, a transition scheme is proposed to avoid artificial wave reflection at the interface of MD and SMD regions. The new transition scheme has simple formulation and high efficiency, and the wave reflection can be well suppressed. Secondly, an adaptive scheme is proposed to automatically identify the regions requiring MD simulation. Two adaptive criteria, the centro-symmetry parameter criterion and the displacement criterion, are also proposed. It is found that both the two criteria can achieve good accuracy, but the efficiency of the displacement criterion is much better. The coupling method does not demand reduction in mesh size near the interface, and a multiple time stepping scheme is adopted to ensure high efficiency. Numerical results including wave propagation, nano-indentation, and crack propagation validate the method and show nice accuracy. This article is protected by copyright. All rights reserved.

Motivated by nano-scale experimental evidence on the dispersion characteristics of materials with a lattice structure, a new multi-scale gradient elasticity model is developed. In the framework of gradient elasticity, the *simultaneous* presence of acceleration- and strain-gradients has been denoted as *dynamic consistency*. This model represents an extension of an earlier dynamically consistent model with an additional micro-inertia contribution to improve the dispersion behaviour. The model can therefore be seen as an enhanced dynamic extension of the Aifantis 1992 strain-gradient theory for statics obtained by including two acceleration gradients in addition to the strain gradient. Compared to the previous dynamically consistent model, the additional micro-inertia term is found to improve the prediction of wave dispersion significantly and, more importantly, requires *no extra computational cost*. The fourth-order equations are rewritten in two sets of symmetric second-order equations so that
-continuity is sufficient in the finite element implementation. Two sets of unknowns are identified as the *microstructural* and *macrostructural* displacements, thus highlighting the multi-scale nature of the present formulation. The associated energy functionals and variationally consistent boundary conditions are presented, after which the finite element equations are derived. Considerable improvements over previous gradient models are observed as confirmed by two numerical examples. This article is protected by copyright. All rights reserved.

Element locking is often seen in homogenized models of elastic fiber-reinforced materials, and splitting the material compliance into two separate terms isolates troublesome strain modes. Once isolated, the locking modes can be addressed with tailored integration schemes or the opportune introduction of field variables. The canonical application of this approach is seen in the dilatational-deviatoric split used to treat so-called ‘volumetric locking.’ In the present work, we invoke the spectral decomposition of the material compliance to provide a generalized split. Doing so naturally parses the response into six independent strain modes, with varying propensity for locking.

This split can be used to generalize fundamental techniques, such as Selective Reduced Integration (SRI) and the B-bar method. This broadened approach works to remedy locking suffered by lower order finite elements used to discretize troublesome materials. Applying these generalized methods to achieve the dilational-deviatoric split is trivial. However, the compliance spectrum's ability to naturally isolate stiff material response modes makes it a uniquely valuable tool for use on homogenized anisotropic materials. Applying the split, defined by only the first compliance mode, has given rise to the generalized methods, which have proven effective in unlocking finite element models of anisotropic materials [1].

In the present work, the generalization is broadened to treat more than one constrained mode. While treating six modes is equivalent to simple reduced integration techniques, up to five compliance modes are now separated for advantageous treatment. However, some attention must be paid to the stability of the resulting finite element stiffness matrices. We focus here on the treatment of two principal compliance modes. These ‘two-mode’ applications of the generalized B-bar method are shown to be a more robust default treatment of linear hexahedral elements than is provided by classical SRI. This is achieved with a negligible computational overhead. A framework for assessing element stability is delineated and commonly arising instabilities are analyzed. This article is protected by copyright. All rights reserved.

Two-phase flows composed of fluids exhibiting different microscopic structure are an important class of engineering materials. The dynamics of these flows are determined by the coupling among three different length scales: microscopic inside each component, mesoscopic interfacial morphology and macroscopic hydrodynamics. Moreover, in the case of complex fluids composed by the mixture between isotropic (newtonian fluid) and nematic (liquid crystal) flows, its interfaces exhibit novel dynamics due to anchoring effects of the liquid crystal molecules on the interface.

Firstly, we have introduced a new differential problem to model Nematic-Isotropic mixtures, taking into account viscous, mixing, nematic and anchoring effects and reformulating the corresponding stress tensors in order to derive a dissipative energy law. Then, we provide two new linear unconditionally energy-stable splitting schemes. Moreover, we present several numerical simulations in order to show the efficiency of the proposed numerical schemes and the influence of the different types of anchoring effects in the dynamics of the system. Copyright © 2016 John Wiley & Sons, Ltd.

We propose a reformulation of the composite tetrahedral finite element first introduced by Thoutireddy, et al. By choosing a different numerical integration scheme, we obtain an element that is more accurate than the one proposed in the original formulation. We also show that in the context of Lagrangian approaches, the gradient and projection operators derived from the element reformulation admit fully analytic expressions, which offer a significant improvement in terms of accuracy and computational expense. For plasticity applications, a mean dilatation approach on top of the underlying Hu-Washizu variational principle proves effective for the representation of isochoric deformations. The performance of the reformulated element is demonstrated by hyperelastic and inelastic calculations. Copyright © 2016 John Wiley & Sons, Ltd.

The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of Statistical Volume Elements (SVEs). Since conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modeled by conventional cohesive interface elements as well as crack propagation modeled by means of the eXtended Finite Element Method (XFEM) in combination with the concept of material forces. Copyright © 2016 John Wiley & Sons, Ltd.

The macroscopic behaviour of materials is affected by their inner micro-structure. Elementary considerations based on the arrangement, and the physical and mechanical features of the micro-structure may lead to the formulation of elastoplastic constitutive laws, involving hardening/softening mechanisms and non-associative properties. In order to model the non-linear behaviour of micro-structured materials, the classical theory of time-independent multisurface plasticity is herein extended to Cosserat continua. The account for plastic relative strains and curvatures is made by means of a robust quadratic-convergent projection algorithm, specifically formulated for non-associative and hardening/softening plasticity. Some important limitations of the classical implementation of the algorithm for multisurface plasticity prevent its application for any plastic surfaces and loading conditions. These limitations are addressed in this paper, and a robust solution strategy based on the Singular Value Decomposition technique is proposed. The projection algorithm is then implemented into a finite element formulation for Cosserat continua. A specific finite element is considered, developed for micropolar plates. The element is validated through illustrative examples and applications, showing able performance. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper a mixed variational formulation for the development of energy-momentum consistent (EMC) time-stepping schemes is proposed. The approach accomodates mixed finite elements based on a Hu-Washizu type variational formulation in terms of displacements, Green-Lagrangian strains und conjugated stresses. The proposed discretization in time of the mixed variational formulation under consideration yields an EMC scheme in a natural way. The newly developed methodology is applied to a high-performance mixed shell finite element. The previously observed robustness of the mixed finite element formulation in equilibrium iterations extends to the transient regime due to the EMC discretization in time. Copyright © 2016 John Wiley & Sons, Ltd..

In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP). This article is protected by copyright. All rights reserved.

This paper introduces and validates a new prediction of sensor noise propagation from images of randomly marked surfaces to displacement maps obtained by Digital Image Correlation (DIC). Images are indeed often affected by sensor noise, which propagates to DIC output. We consider here the 2D global DIC (G-DIC), for which this output is the in-plane displacement calculated at a set of nodes. Predictive formula for the resolution of the displacement at these nodes is already available in the literature. The contribution of the present paper is to revisit this formula to take into account the interpolation required by sub-pixel displacement. A generalization is also proposed to predict the displacement resolution throughout the field of view. It is then extended to several kinds of DIC. The correlation procedure is thoroughly described in order to emphasize the role of the interpolation. A numerical assessment on synthetic data validates the new prediction and shows the improvement brought about by the proposed formula. This article is protected by copyright. All rights reserved.

Inhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models have been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finite-element-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom – the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (i) linear shear with gravity, (ii) annular shear flow without gravity, and (iii) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh-independent. This article is protected by copyright. All rights reserved.

The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analyzed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. This article is protected by copyright. All rights reserved.

The analysis of reactive systems in combustion science and technology relies on detailed models comprising many chemical reactions that describe the conversion of fuel and oxidizer into products and the formation of pollutants. Shock-tube experiments are a convenient setting for measuring the rate parameters of individual reactions. The temperature, pressure, and concentration of reactants are chosen to maximize the sensitivity of the measured quantities to the rate parameter of the target reaction. In this study, we optimize the experimental setup computationally by optimal experimental design (OED) in a Bayesian framework. We approximate the posterior probability density functions (pdf) using truncated Gaussian distributions in order to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate, and the covariance is chosen as the negative inverse of the Hessian of the misfit function at the MAP estimate. The model related entities are obtained from a polynomial surrogate. The optimality, quantified by the information gain measures, can be estimated efficiently by a rejection sampling algorithm against the underlying Gaussian probability distribution, rather than against the true posterior. This approach offers a significant error reduction when the magnitude of the invariants of the posterior covariance are comparable to the size of the bounded domain of the prior. We demonstrate the accuracy and superior computational efficiency of our method for shock-tube experiments aiming to measure the model parameters of a key reaction which is part of the complex kinetic network describing the hydrocarbon oxidation. In the experiments, the initial temperature and fuel concentration are optimized with respect to the expected information gain in the estimation of the parameters of the target reaction rate. We show that the expected information gain surface can change its “shape" dramatically according to the level of noise introduced into the synthetic data. The information that can be extracted from the data saturates as a logarithmic function of the number of experiments, and few experiments are needed when they are conducted at the optimal experimental design conditions. Furthermore, inversion of the legacy data indicates the validity and robustness of our designs. This article is protected by copyright. All rights reserved.

This paper proposes a first step towards a framework to develop shell elements applicable to any deformation regime. Here, we apply it to the large and moderate deformations of, respectively, plates and shells, showing with standard benchmarks that the resulting low-order discretization is competitive against the best elements for either membrane- or bending-dominated scenarios. Additionally, we propose a new test for measuring membrane locking, which highlights the mesh-independence properties of our element. Our strategy is based on building a discrete model that mimics the smooth behavior by construction, rather than discretizing a smooth energy. The proposed framework consists of two steps: (i) defining a discrete kinematics by means of constraints and (ii) formulating an energy that vanishes on such a constraint manifold. We achieve (i) by considering each triangle as a *tensegrity* structure, constructed to be unstretchable but bendable isometrically (in a discrete sense). We then present a choice for (ii) based on assuming a linear strain field on each triangle, using tools from differential geometry for coupling the discrete membrane energy with our locking-free kinematic description. We argue that such a locking-free element is only a member of a new family that can be created using our framework (i)-(ii). This article is protected by copyright. All rights reserved.

We present three velocity-based Updated Lagrangian formulations for standard and quasi-incompressible hypoelastic-plastic solids. Three finite elements, named V, VP and VPS elements are derived and tested for benchmark for non-linear solid mechanics problems. The V-element is based on a standard velocity approach, while for the VP and VPS elements a mixed velocity-pressure formulation is used. The two-field problem is solved via a two-step Gauss-Seidel partitioned iterative scheme. First the momentum equations are solved in terms of velocity increments, as for the V-element. Then the constitutive relation for the pressure is solved using the updated velocities obtained at the previous step. For the VPS-element the equation for the pressure is stabilized using the Finite Calculus (FIC) method in order to solve problems involving quasi-incompressible materials. All the solid elements are validated by solving 2D and 3D benchmark problems in statics as in dynamics. This article is protected by copyright. All rights reserved.

We develop a computational framework that captures the microfracture processes leading to shear band bifurcation in porous crystalline rocks. The framework consists of computational homogenization on a representative elementary volume (REV) that upscales the pore-scale microfracture processes to the continuum scale. The assumed enhanced strain (AES) finite element approach is used to capture the discontinuous displacement field generated by the microfractures. Homogenization at the continuum scale results in incrementally nonlinear material response, in which the overall constitutive tangent tensor varies with the stress state as well as with the loading direction. Continuum bifurcation detects the formation of a shear band on the REV level; multi-dimensional strain probes, necessitated by the incremental nonlinearity of the overall constitutive response, determine the most critical orientation for shear band bifurcation. Numerical simulations focus on microfracturing at the pore scale with either predominant interface separation or predominant interface contact modes. Results suggest a non-associative overall plastic flow and shear band bifurcation that depends on the microfracture length and the characteristic sliding distance related to slip weakening. This article is protected by copyright. All rights reserved.

The static formulation of elastic shakedown analysis, based upon Melan's lower bound theorem, can essentially be viewed as a robust optimization problem. This paper discusses an advantage that is enjoyed by taking this perspective. Specifically, we assume the von Mises yield criterion and an ellipsoidal load domain. In this setting, the shakedown analysis problem, which is viewed as robust second-order cone programming, can be recast as semidefinite programming. This article is protected by copyright. All rights reserved.

We propose a method for efficient evaluation of surface integrals arising in boundary element methods for three-dimensional Helmholtz problems (with real positive wavenumber *k*), modelling wave scattering and/or radiation in homogeneous media. To reduce the number of degrees of freedom required when *k* is large, a common approach is to include in the approximation space oscillatory basis functions, with support extending across many wavelengths. A difficulty with this approach is that it leads to highly oscillatory surface integrals whose evaluation by standard quadrature would require at least O(*k*^{2}) quadrature points. Here, we use equivalent contour integrals developed for aperture scattering in optics to reduce this requirement to O(*k*), and possible extensions to reduce it further to O(1) are identified. The contour integral is derived for arbitrary shaped elements, but its application is limited to planar elements in many cases. In addition, the transform regularises the singularity in the surface integrand caused by the Green's function, including for the hyper-singular case under appropriate conditions. An open-source Matlab™ code library is available to demonstrate our routines.

In this work, the consequences of using several different Discrete Element granular assemblies for the representation of the microscale structure, in the framework of multiscale modelling, have been investigated. The adopted modelling approach couples, through computational homogenization, a macroscale continuum with microscale discrete simulations. Several granular assemblies were used depending on the location in the macroscale Finite Element mesh. The different assemblies were prepared independently as being representative of the same material but their geometrical differences imply slight differences in their response to mechanical loading. The role played by the micro-assemblies, with weaker macroscopic mechanical properties, on the initiation of strain localization in biaxial compression tests is demonstrated and illustrated by numerical modelling of different macroscale configurations. This article is protected by copyright. All rights reserved.

Moulinec and Suquet introduced FFT-based homogenization in 1994, and twenty years later, their approach is still effective for evaluating the homogenized properties arising from the periodic cell problem. This paper builds on the author's (2013) variational reformulation approximated by trigonometric polynomials establishing two numerical schemes: Galerkin approximation (Ga) and a version with numerical integration (GaNi). The latter approach, fully equivalent to the original Moulinec-Suquet algorithm, was used to evaluate guaranteed upper-lower bounds on homogenized coefficients incorporating a closed-form double grid quadrature. Here, these conceptsred, based on the primal and the dual formulations, are employed for the Ga scheme. blueredFor the same computational effort, the Ga outperforms the GaNi with more accurate guaranteed bounds and more predictable numerical behaviors. Quadrature technique leading to block-sparse linear systems is extended here to materials defined via high-resolution images in a way which allows for effective treatment using the FFT. redMemory demands are reduced by a reformulation of the double to the original grid scheme using FFT shifts. blueMinimization of the bounds during iterations of conjugate gradients is effective, particularly when incorporating a solution from a coarser grid. The methodology presented here for the scalar linear elliptic problem could be extended to more complex frameworks. This article is protected by copyright. All rights reserved.

The paper aims at proposing a new strategy for real-time identification or updating of structural mechanics models defined as dynamical systems. The main idea is to introduce the modified constitutive relation error concept which is a practical tool that enables to efficiently solve identification problems with highly corrupted data, into the Kalman filtering which is a classical framework for data assimilation. Furthermore, a PGD-based model reduction method is performed in order to optimize capabilities of the *online* updating strategy. Performances of the proposed approach, in terms of robustness gain and computational cost reduction, are illustrated on several unsteady thermal applications. This article is protected by copyright. All rights reserved.

In this paper we present a homogenization approach that can be used in the geometrically nonlinear regime for stress- and strain-driven homogenization and even a combination of both. Special attention is paid to the straightforward implementation in combination with the finite-element method. The formulation follows directly from the principle of virtual work, the periodic boundary conditions and the Hill-Mandel principle of macro-homogeneity. The periodic boundary conditions are implemented using the Lagrange multiplier method to link macroscopic strain to the boundary displacements of the computational model of a representative volume element. We include the macroscopic strain as a set of additional degrees of freedom in the formulation. Via the Lagrange multipliers, the macroscopic stress naturally arises as the associated ‘forces’ that are conjugate to the macroscopic strain ‘displacements’. In contrast to most homogenization schemes, the second Piola-Kirchhoff stress and Green-Lagrange strain have been chosen for the macroscopic stress and strain measures in this formulation. The usage of other stress and strain measures such as the first Piola-Kirchhoff stress and the deformation gradient is discussed in the appendix. This article is protected by copyright. All rights reserved.

Incompressible free-surface flow is a common assumption for the modelling of water waves. Connected with the aim to develop very large floating platforms, air chamber supported floating structures have attracted considerable research interest in the past. Such structures are carried by air entrapped in chambers formed by stiff, vertical walls. In order to model these type of structures, the interactions between surface gravity waves and compressible air must be taken into account. If the payload requirements for air chamber supported structures are low enough, the air chambers may be formed by flexible membrane cylinders. In such systems, pressure variations can lead to considerable changes in chamber volume. Therefore, the flexibility of the bounding structures must be taken into account.

We present a modelling strategy to tackle the fully coupled problem of compressible gas in a flexible chamber, and incompressible free-surface flow in an unbounded domain. The governing equations and boundary conditions are described, and solved by the finite element method. A perfectly matched layer is used to obtain a solution for an unbounded domain. Finally, the numerical implementation is validated by various test cases. This article is protected by copyright. All rights reserved.

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a framework where we can swap Newton and DD, so that we solve independent nonlinear problems for each substructure and linear condensed interface problems. The objective is to decrease the number of communications between subdomains and to improve parallelism. Depending on the interface condition, we derive several formulations which are not equivalent, contrarily to the linear case. Primal, dual and mixed variants are described and assessed on a simple plasticity problem. This article is protected by copyright. All rights reserved.

The present work addresses shape sensitivity analysis and optimization in two-dimensional elasticity with a regularised isogeometric boundary element method (IGABEM). NURBS are used both for the geometry and the basis functions to discretize the regularised boundary integral equations. With the advantage of tight integration of design and analysis, the application of IGABEM in shape optimziation reduces the mesh generation/regeneration burden greatly. The work is distinct from the previous literatures in IGABEM shape optimization mainly in two aspects: 1) the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations, eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives, which were the main implementation difficulty in IGABEM, and 2) although based on the same CAD model, the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh, thus achieving a balance between less design variables for efficiency and refined mesh for accuracy. This technique was initially used in isogeometric finite element method and was incorporated into the present IGABEM implementation. This article is protected by copyright. All rights reserved.

In this paper, based on the general stress-strain relationship, displacement and stress boundary-domain integral equations are established for single medium with varying material properties. From the established integral equations, single interface integral equations are derived for solving general multi-medium mechanics problems by making use of the variation feature of the material properties. The displacement and stress interface integral equations derived in this paper can be applied to solve non-homogeneous, anisotropic, and non-linear multi-medium problems in a unified way. By imposing some assumptions on the derived integral equations, detailed expressions for some specific mechanics problems are deduced, and a few numerical examples are given to demonstrate the correctness and robustness of the derived displacement and stress interface integral equations. This article is protected by copyright. All rights reserved.

The mechanics of the interaction between a fluid and a soft interface undergoing large deformations appear in many places, such as in biological systems or industrial processes. We present an Eulerian approach that describes the mechanics of an interface and its interactions with a surrounding fluid via the so-called Navier boundary condition. The interface is modeled as a curvilinear surface with arbitrary mechanical properties across which discontinuities in pressure and tangential fluid velocity can be accounted for using a modified version of the Extended Finite element Method (X-FEM). The coupling between the interface and the fluid is enforced through the use of Lagrange multipliers. The tracking and evolution of the interface is then handled in a Lagrangian step with the Grid Based Particle method. We show that this method is ideal to describe large membrane deformations and Navier boundary conditions on the interface with velocity/pressure discontinuities. The validity of the model is assessed by evaluating the numerical convergence for a axisymmetrical flow past a spherical capsule with various surface properties. We show the effect of slip length on the shear flow past a two-dimensional capsule and simulate the compression of an elastic membrane lying on a viscous fluid substrate. This article is protected by copyright. All rights reserved.

The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method designed to study systems governed by Helmholtz-like equations. It uses wave functions to represent the solution inside elements, which reduces the dispersion error compared to classical polynomial approaches but the resulting system is prone to be ill conditioned. This paper gives a simple and original presentation of the VTCR using the discontinuous Galerkin framework and it traces back the ill-conditioning to the accumulation of eigenvalues near zero for the formulation written in terms of wave amplitude. The core of this paper presents an efficient solving strategy that overcomes this issue. The key element is the construction of a search subspace where the condition number is controlled at the cost of a limited decrease of attainable precision. An augmented LSQR solver is then proposed to solve efficiently and accurately the complete system. The approach is successfully applied to different examples. This article is protected by copyright. All rights reserved.

The FE^{2} method [1, 2] is a renown computational multiscale simulation technique for solid materials with fine scale microstructure. It allows for the accurate prediction of the mechanical behavior of structures made of heterogeneous materials with nonlinear material behavior. However, the FE^{2} method leads to excessive CPU time and storage requirements, even for academic two-dimensional problems. In order to allow for realistic three-dimensional two-scale simulations, a significant reduction of the CPU *and* memory usage is required. For this purpose, the authors have recently proposed a reduced basis homogenization scheme based on a mixed incremental variational principle [3]. The approach exploits the potential structure of Generalized Standard Materials [4]. Thereby, important speed-ups and memory savings can be achieved. Using high-performance GPUs the reduced basis method can be further accelerated [5]. In the present contribution our previous works are combined and extended to form the FE^{2} Reduced method: the FE^{2R}. The FE^{2R} can be used to simulate three-dimensional structural problems with consideration of the nonlinearity and microstructure of the underlying material at acceptable computational cost. Thereby, it allows for a new level of complexity in nonlinear multiscale simulations. Numerical examples illustrate the capabilities of the chosen approach. This article is protected by copyright. All rights reserved.

The basic principles of the discrete duality and non linear monotone finite volume methods are combined in order to obtain a new monotone non-linear finite volume method for the approximation of diffusion operators on general meshes. Numerical results highlight both the second order accuracy of this method on general meshes and its capability to deal with challenging anisotropic diffusion problems on various computational domains. This article is protected by copyright. All rights reserved.

The hybrid-mixed assumed natural strain four-node quadrilateral element using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the plate body *N* not equally spaced SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree *N*–1 in the thickness direction permits the presentation of the plate formulation in a very compact form. The SaS are located at Chebyshev polynomial nodes that allow one to minimize uniformly the error due to the Lagrange interpolation. To avoid shear locking and have no spurious zero energy modes, the assumed natural strain concept is employed. The developed hybrid-mixed four-node quadrilateral plate element passes patch tests and exhibits a superior performance in the case of coarse distorted mesh configurations. It can be useful for the 3D stress analysis of thin and thick plates because the SaS formulation gives the possibility to obtain solutions with a prescribed accuracy, which asymptotically approach the 3D exact solutions of elasticity as the number of SaS tends to infinity. Copyright © 2016 John Wiley & Sons, Ltd.

The finite cell method (FCM) is an immersed domain finite element method that combines higher-order non-boundary-fitted meshes, weak enforcement of Dirichlet boundary conditions, and adaptive quadrature based on recursive subdivision. Because of its ability to improve the geometric resolution of intersected elements, it can be characterized as an *immersogeometric* method. In this paper, we extend the FCM, so far only used with Cartesian hexahedral elements, to higher-order non-boundary-fitted tetrahedral meshes, based on a reformulation of the octree-based subdivision algorithm for tetrahedral elements. We show that the resulting TetFCM scheme is fully accurate in an immersogeometric sense, that is, the solution fields achieve optimal and exponential rates of convergence for *h*-refinement and *p*-refinement, if the immersed geometry is resolved with sufficient accuracy. TetFCM can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions. Its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase-field fracture analysis of a human femur bone. Copyright © 2016 John Wiley & Sons, Ltd.

We construct new robust and efficient preconditioned generalized minimal residual solvers for the monolithic linear systems of algebraic equations arising from the finite element discretization and Newton's linearization of the fully coupled fluid–structure interaction system of partial differential equations in the arbitrary Lagrangian–Eulerian formulation. We admit both linear elastic and nonlinear hyperelastic materials in the solid model and cover a large range of flows, for example, water, blood, and air, with highly varying density. The preconditioner is constructed in form of
, where
,
, and
are proper approximations to the matrices *L*, *D*, and *U* in the *LDU* block factorization of the fully coupled system matrix, respectively. The inverse of the corresponding Schur complement is approximated by applying a few cycles of a special class of algebraic multigrid methods to the perturbed fluid sub-problem, which is obtained by modifying corresponding entries in the original fluid matrix with an explicitly constructed approximation to the exact perturbation coming from the sparse matrix–matrix multiplications. The numerical studies presented impressively demonstrate the robustness and the efficiency of the preconditioner proposed in the paper. Copyright © 2016 John Wiley & Sons, Ltd.

We introduce Lagrange extraction and projection that link a *C*^{0} nodal basis with a smooth B-spline basis. Our technology is equivalent to Bézier extraction and projection but offers an alternative implementation based on the interpolatory property of nodal basis functions. The Lagrange extraction operator can be constructed by simply evaluating B-spline basis functions at nodal points and eliminates the need for introducing Bernstein polynomials as new shape functions. The Lagrange projection operator is defined as the inverse of the Lagrange extraction operator and directly relates function values at nodal points to element-level B-spline coefficients of a local interpolant. For geometries based on polynomial B-splines, our technology allows the implementation of isogeometric analysis in standard nodal finite element codes with simple algorithms and minimal intrusion. Copyright © 2016 John Wiley & Sons, Ltd.

Linear buckling constraints are important in structural topology optimization for obtaining designs that can support the required loads without failure. During the optimization process, the critical buckling eigenmode can change; this poses a challenge to gradient-based optimization and can require the computation of a large number of linear buckling eigenmodes. This is potentially both computationally difficult to achieve and prohibitively expensive. In this paper, we motivate the need for a large number of linear buckling modes and show how several features of the block Jacobi conjugate gradient (BJCG) eigenvalue method, including optimal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts, can be used to efficiently and robustly compute a large number of buckling eigenmodes. This paper also introduces linear buckling constraints for level-set topology optimization. In our approach, the velocity function is defined as a weighted sum of the shape sensitivities for the objective and constraint functions. The weights are found by solving an optimization sub-problem to reduce the mass while maintaining feasibility of the buckling constraints. The effectiveness of this approach in combination with the BJCG method is demonstrated using a 3D optimization problem. Copyright © 2016 John Wiley & Sons, Ltd.

A method is proposed to compute the response of highly heterogeneous structures by constructing homogenized models when no scale separation can be assumed. The technique is based on an extended homogenization scheme where the averaging operators are replaced by linear filters to cut off fine scale fluctuations, while maintaining locally varying mechanical fields with larger wavelength. As a result, the constitutive law at an intermediate scale, called mesoscale, arises to be naturally nonlocal by construction, where the kernel operator is fully constructed by computations on the unit cell associated with the microstructure. A displacement-based numerical strategy is developed to implement the technique in a classical finite element framework and does not require higher-order elements. The methodology is applied to construct simplified models of heterogeneous structures subjected to loads, which have a characteristic wavelength comparable with the dimensions of the heterogeneities or in presence of strong strain localization as in cracked heterogeneous structures. Copyright © 2016 John Wiley & Sons, Ltd.

In this article, we introduce a fast, memory efficient and robust sparse preconditioner that is based on a direct factorization scheme for sparse matrices arising from the finite-element discretization of elliptic partial differential equations. We use a fast (but approximate) multifrontal approach as a preconditioner and use an iterative scheme to achieve a desired accuracy. This approach combines the advantages of direct and iterative schemes to arrive at a fast, robust, and accurate preconditioner. We will show that this approach is faster (∼2×) and more memory efficient (∼2–3×) than a conventional direct multifrontal approach. Furthermore, we will demonstrate that this preconditioner is both faster and more effective than other preconditioners such as the incomplete LU preconditioner. Specific speedups depend on the matrix size and improve as the size of the matrix increases. The preconditioner can be applied to both structured and unstructured meshes in a similar manner. We build on our previous work and utilize the fact that dense frontal and update matrices, in the multifrontal algorithm, can be represented as hierarchically off-diagonal low-rank matrices. Using this idea, we replace all large dense matrix operations in the multifrontal elimination process with *O*(*N*) hierarchically off-diagonal low-rank operations to arrive at a faster and more memory efficient factorization scheme. We then use this direct factorization method at low accuracies as a preconditioner and apply it to various real-life engineering test cases. Copyright © 2016 John Wiley & Sons, Ltd.

The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo-mechanical problems. In particular, the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes, and thermal effects.

The framework of the numerical scheme is based on the particle finite element method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a *Delaunay* triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (*α* − *s**h**a**p**e* method), in this work, the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function.

The description of the thermo-mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u-p mixed formulation, with a stabilization of the pressure term via the polynomial pressure projection, is proposed.

One of the novelties of this work is the use of a combination between the isothermal split and the so-called IMPL-EX hybrid integration technique to enhance the robustness and reduce the typical iteration number of the fully implicit Newton–Raphson solution algorithm.

The new set of numerical tools implemented in the PFEM algorithm, including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo-mechanical problems.

Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking-free element type and different time integration schemes for thermo-mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example. Copyright © 2016 John Wiley & Sons, Ltd.

A robust and efficient dynamic grid strategy based on an overset grid coupled with mesh deformation technique is proposed for simulating unsteady flow of flapping wings undergoing large geometrical displacement. The dynamic grid method was implemented using a hierarchical unstructured overset grid locally coupled with a fast radial basis function (RBF)-based mapping approach. The hierarchically organized overset grid allows transferring the grid resolution for multiple blocks and overlapping/embedding the meshes. The RBF-based mapping approach is particularly highlighted in this paper in view of its considerable computational efficiency compared with conventional RBF evaluation. The performance of the proposed dynamic mesh strategy is demonstrated by three typical unsteady cases, including a rotating rectangular block in a fixed domain, a relative movement between self-propelled fishes and the X-wing type flapping-wing micro air vehicle DelFly, which displays the clap-and-fling wing-interaction phenomenon on both sides of the fuselage. Results show that the proposed method can be applied to the simulation of flapping wings with satisfactory efficiency and robustness. Copyright © 2016 John Wiley & Sons, Ltd.

In this article, we propose a new approach for model reduction of parameterized partial differential equations (PDEs) by a locally weighted proper orthogonal decomposition (LWPOD) method. The presented approach is particularly suited for large-scale nonlinear systems characterized by parameter variations. Instead of using a global basis to construct a global reduced model, LWPOD approximates the original system by multiple local reduced bases. Each local reduced basis is generated by the singular value decomposition of a weighted snapshot matrix. Compared with global model reduction methods, such as the classical proper orthogonal decomposition, LWPOD can yield more accurate solutions with a fixed subspace dimension. As another contribution, we combine LWPOD with the chord iteration to solve elliptic PDEs in a computationally efficient fashion. The potential of the method for achieving large speedups while maintaining good accuracy is demonstrated for both elliptic and parabolic PDEs in a few numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

Computational modeling remains key to the acoustic design of various applications, but it is constrained by the cost of solving large Helmholtz problems at high frequencies. This paper presents an efficient implementation of the high-order finite element method (FEM) for tackling large-scale engineering problems arising in acoustics. A key feature of the proposed method is the ability to select automatically the order of interpolation in each element so as to obtain a target accuracy while minimizing the cost. This is achieved using a simple local *a priori* error indicator. For simulations involving several frequencies, the use of hierarchical shape functions leads to an efficient strategy to accelerate the assembly of the finite element model. The intrinsic performance of the high-order FEM for 3D Helmholtz problem is assessed, and an error indicator is devised to select the polynomial order in each element. A realistic 3D application is presented in detail to demonstrate the reduction in computational costs and the robustness of the *a priori* error indicator. For this test case, the proposed method accelerates the simulation by an order of magnitude and requires less than a quarter of the memory needed by the standard FEM. Copyright © 2015 John Wiley & Sons, Ltd.

Discrete element codes use complex geometric solid particles, so it is necessary to integrate three-dimensional rigid-body rotation correctly with external torque. This article presents an interpretation of the Leapfrog scheme. We begin with some rotation formulae before presenting an efficient and high-order recurrent Taylor series method for rotation. Integrating this method with Leapfrog interpretation provides a complete scheme for rotational motion with external torque. This new Leapfrog scheme has been integrated into the CeaMka3D Discrete Element code, and we present some verifications and simulations to illustrate the capabilities of this scheme. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, the non-isothermal elasto-plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo-hydro-mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the hybrid mixture theory. A computationally efficient reduced formulation of the macroscopic balance equations that neglects the relative acceleration of the fluids, and the convective terms is adopted. The modified effective stress state is limited by the Drucker–Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non-linear set of equations is solved by the Newton method with a monolithic approach. Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A numerical study of the regularization properties of the finite element model is shown and discussed. A non-isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed. Copyright © 2015 John Wiley & Sons, Ltd.

A computational homogenization scheme is developed to model heterogeneous hyperelastic materials undergoing large deformations. The homogenization scheme is based on a so-called computational continua formulation in which the macro-scale model is assumed to consist of disjoint unit cells. This formulation adds no higher-order boundary conditions and extra degrees of freedom to the problem. A computational procedure is presented to calculate the macroscopic quantities from the solution of the representative volume element boundary value problem. The proposed homogenization scheme is verified against a direct numerical simulation. It is also shown that the computational cost of the proposed model is lower than that of standard homogenization schemes. Copyright © 2015 John Wiley & Sons, Ltd.

This study documents the first attempt to extend the singular boundary method, a novel meshless boundary collocation method, for the solution of 3D elasticity problems. The singular boundary method involves a coupling between the regularized BEM and the method of fundamental solutions. The main idea here is to fully inherit the dimensionality and stability advantages of the former and the meshless and integration-free attributes of the later. This makes it particularly attractive for problems in complex geometries and three dimensions. Four benchmark 3D problems in linear elasticity are well studied to demonstrate the feasibility and accuracy of the proposed method. The advantages, disadvantages, and potential applications of the proposed method, as compared with the FEM, BEM, and method of fundamental solutions, are also examined and discussed. Copyright © 2015 John Wiley & Sons, Ltd.

This work addresses the use of the topology optimization approach to the design of robust continuum structures under the hypothesis of uncertainties with known second-order statistics. To this end, the second-order perturbation approach is used to model the response of the structure, and the midpoint discretization technique is used to discretize the random field. The objective function is a weighted sum of the expected compliance and its standard deviation. The optimization problem is solved using a traditional optimality criteria method. It is shown that the correlation length plays an important role in the obtained topology and statistical moments when only the minimization of the standard deviation is considered, resulting in more and thinner reinforcements as the correlation length decreases. It is also shown that the minimization of the expected value is close to the minimization of the deterministic compliance for small variations of Young's modulus. Copyright © 2015 John Wiley & Sons, Ltd.

A new technique for sharp-interface modeling of dendritic solidification is proposed using a meshfree interface finite element method such that the liquid–solid interface is represented implicitly and allowed to arbitrarily intersect the finite elements. At the interface-embedded elements, meshfree interface points without connectivity are imposed directly at the zero level set while meshfree interpolants are constructed using radial basis functions. This ensures both the partition of unity and the Kronecker delta properties are satisfied allowing for precise and easy imposition of Dirichlet boundary conditions at the interface. The constructed meshfree interpolants are also used for solving a variational level set equation based on the Ginzburg–Landau energy functional minimization such that reinitialization is completely eliminated and fast marching algorithms for interfacial velocity extension are not necessary resulting in an efficient algorithm with excellent volume conservation. The meshfree interface finite element method is used for modeling dendritic solidification in a pure melt where it is found suitable in handling the complex interfacial dynamics often encountered in dendritic growth. Mathematical formulation and implementation followed by numerical results and analysis will be presented and discussed. Copyright © 2015 John Wiley & Sons, Ltd.

We consider the efficient numerical solution of the three-dimensional wave equation with Neumann boundary conditions via time-domain boundary integral equations. A space-time Galerkin method with *C*^{∞}-smooth, compactly supported basis functions in time and piecewise polynomial basis functions in space is employed. We discuss the structure of the system matrix and its efficient parallel assembly. Different preconditioning strategies for the solution of the arising systems with block Hessenberg matrices are proposed and investigated numerically. Furthermore, a C++ implementation parallelized by OpenMP and MPI in shared and distributed memory, respectively, is presented. The code is part of the boundary element library BEM4I. Results of numerical experiments including convergence and scalability tests up to a thousand cores on a cluster are provided. The presented implementation shows good parallel scalability of the system matrix assembly. Moreover, the proposed algebraic preconditioner in combination with the FGMRES solver leads to a significant reduction of the computational time. Copyright © 2015 John Wiley & Sons, Ltd.

Magnetorheological elastomers are materials with a composite microstructure that consists of an elastomeric matrix and magnetizable inclusions. Because of the magnetic inclusions, magnetorheological elastomers are able to change their properties under magnetic field. Thereby, their effective behavior strongly depends on the microstructure. This calls for *homogenization strategies* to characterize their macroscopic response. However, for arbitrary macroscopic bodies, this is a non-trivial task. The main difficulty stems from the fact that a magnetic body interacts with its surrounding and thus perturbs the magnetic field it is subjected to. In a multiscale simulation, this interaction has to be accounted for through a physically sound prescription of *magnetic boundary conditions*. Thus, the goal of this contribution is to establish a two-scale homogenization framework that allows for both (i) the incorporation of the microstructure into the macroscopic simulation and (ii) the application of experimentally motivated boundary conditions on arbitrary macroscopic bodies. We show the capabilities of the approach in several numerical studies, in which we analyze the effective behavior of different specimens. Depending on their microstructure, we observe a contraction or extension of the specimens and find magnetically induced stiffening or weakening. All numerical predictions are in good qualitative agreement with experimental measurements. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we present an approach for robust compliance topology optimization under volume constraint. The compliance is evaluated considering a point-wise worst-case scenario. Analogously to sequential optimization and reliability assessment, the resulting robust optimization problem can be decoupled into a deterministic topology optimization step and a reliability analysis step. This procedure allows us to use topology optimization algorithms already developed with only small modifications. Here, the deterministic topology optimization problem is addressed with an efficient algorithm based on the topological derivative concept and a level-set domain representation method. The reliability analysis step is handled as in the performance measure approach. Several numerical examples are presented showing the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

The generation of a set of particles with high initial volume fraction is a major problem in the context of discrete element simulations. Advancing front algorithms provide an effective means to generate dense packings when spherical particles are assumed. The objective of this paper is to extend an advancing front algorithm to a wider class of particles with generic size and shape. In order to get a dense packing, each new particle is placed in contact with other two (or three in 3D) particles of the advancing front. The contact problem is solved analytically using wrapping intersection technique. The results presented herein will be useful in the application of these algorithms to a wide variety of practical problems. Examples of geometric models for applications to biomechanics and cutting tools are presented. Copyright © 2015 John Wiley & Sons, Ltd.

An efficient symmetric Lanczos method for the solution of vibro-acoustic eigenvalue problems is presented in this paper. Although finite element discretization results in real but nonsymmetric system matrices, we show that an efficient iteration scheme on a symmetric representation can be built up by using a transformation matrix. In order to decrease the numerical costs of the orthogonalizations performed, we propose to use a partial orthogonalization scheme for the symmetric case. The proposed method is tested on two large problems in order to demonstrate its efficiency and accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

Convergent and stable domain integration that is also computationally efficient remains a challenge for Galerkin meshfree methods. High order quadrature can achieve stability and optimal convergence, but it is prohibitively expensive for practical use. On the other hand, low order quadrature consumes much less CPU but can yield non-convergent, unstable solutions. In this work, an accelerated, convergent, and stable nodal integration is developed for the reproducing kernel particle method. A stabilization scheme for nodal integration is proposed based on implicit gradients of the strains at the nodes that offers a computational cost similar to direct nodal integration. The method is also formulated in a variationally consistent manner, so that optimal convergence is achieved. A significant efficiency enhancement over a comparable stable and convergent nodal integration scheme is demonstrated in a complexity analysis and in CPU time studies. A stability analysis is also given, and several examples are provided to demonstrate the effectiveness of the proposed method for both linear and nonlinear problems. Copyright © 2015 John Wiley & Sons, Ltd.

The ‘model-based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model-based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an *explicit* formulation. These two features make the model-based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either *explicit* or *semi-explicit*, where the former refers to the algorithms with *explicit* difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second-order unconditionally stable parametrically dissipative *semi-explicit* algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model-based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd.

An immersed finite element fluid–structure interaction algorithm with an anisotropic remeshing strategy for thin rigid structures is presented in two dimensions. One specific feature of the algorithm consists of remeshing only the fluid elements that are cut by the solid such that they fit the solid geometry. This approach allows to keep the initial (given) fluid mesh during the entire simulation while remeshing is performed locally. Furthermore, constraints between the fluid and the solid may be directly enforced with both an essential treatment and elements allowing the stress to be discontinuous across the structure. Remeshed elements may be strongly anisotropic. Classical interpolation schemes – inf–sup stable on isotropic meshes – may be unstable on anisotropic ones. We specifically focus on a proper finite element pair choice. As for the time advancing of the fluid–structure interaction solver, we perform a geometrical linearization with a sequential solution of fluid and structure in a backward Euler framework. Using the proposed methodology, we extensively address the motion of a hinged rigid leaflet. Numerical tests demonstrate that some finite element pairs are inf–sup unstable with our algorithm, in particular with a discontinuous pressure. Copyright © 2015 John Wiley & Sons, Ltd.

The concept of a ‘Representative Volume Model’ is used in combination with ‘Equivalent Mechanical Strain’ or Aboudi's ‘Average Strain’ theorem to illustrate how a carbon nanotube reinforced composite material constitutive law for a nano-composite material can be implemented into a finite element program for modeling structural applications. Current methods of modeling each individual composite layer to build up an element composed of carbon nanotube reinforced composite material may not be the best approach for modeling structural applications of this composite. The approach presented here is based upon presentations given at the National Science Foundation-Civil and Mechanical Systems division workshop at John Hopkins University in 2004, which is referred to in this paper as the Williams-Baxter approach. This approach is also used to demonstrate that damage modeling can be included as was suggested in this workshop. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we define the spurious kinematic modes of hybrid equilibrium 2D and 3D simplicial elements of general degree and present the results of studies on the stability of star patches of such elements. The approach used in these studies is based on first establishing the kinematic properties of a pair of elements that share an interface. This approach is introduced by its application to star patches of hybrid equilibrium triangular plate elements for modelling membrane and plate bending problems and then generalised to 3D continua. It is then shown how the existence of spurious kinematic modes depends on the topological and geometrical properties of a patch, as well as on the degree of the polynomial approximation functions of stress and displacement. Copyright © 2015 John Wiley & Sons, Ltd.

The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to enable an easy treatment of complex geometries. A key issue comes from the sensitivity analysis of the structural responses with respect to the design parameters ruling the boundaries. Even if the approach does not imply any mesh modification, the study shows that shape modifications lead to difficulties when the perturbation of the level sets modifies the set of extended finite elements. To circumvent the problem, an analytical sensitivity analysis of the structural system is developed. Differences between the sensitivity analysis using FEM or XFEM are put in evidence. To conduct the sensitivity analysis, an efficient approach to evaluate the so-called velocity field is developed within the XFEM domain. The proposed approach determines a continuous velocity field in a boundary layer around the zero level set using a local finite element approximation. The analytical sensitivity analysis is validated against the finite differences and a semi-analytical approach. Finally, our shape optimization tool for bimaterial structures is illustrated by revisiting the classical problem of the shape of soft and stiff inclusions in plates. Copyright © 2015 John Wiley & Sons, Ltd.

In this study, a post optimization technique for a correction of inaccurate optimum obtained using first-order reliability method (FORM) is proposed for accurate reliability-based design optimization (RBDO). In the proposed method, RBDO using FORM is first performed, and then the proposed second-order reliability method (SORM) is performed at the optimum obtained using FORM for more accurate reliability assessment and its sensitivity analysis. In the proposed SORM, the Hessian of a performance function is approximated by reusing derivatives information accumulated during previous RBDO iterations using FORM, indicating that additional functional evaluations are not required in the proposed SORM. The proposed SORM calculates a probability of failure and its first-order and second-order stochastic sensitivity by applying the importance sampling to a complete second-order Taylor series of the performance function. The proposed post optimization constructs a second-order Taylor expansion of the probability of failure using results of the proposed SORM. Because the constructed Taylor expansion is based on the reliability method more accurate than FORM, the corrected optimum using this Taylor expansion can satisfy the target reliability more accurately. In this way, the proposed method simultaneously achieves both efficiency of FORM and accuracy of SORM. Copyright © 2015 John Wiley & Sons, Ltd.

In this study, we propose an effective method to estimate the reliability of finite element models reduced by the automated multi-level substructuring (AMLS) method. The proposed error estimation method can accurately predict relative eigenvalue errors in reduced finite element models. A new, enhanced transformation matrix for the AMLS method is derived from the original transformation matrix by properly considering the contribution of residual substructural modes. The enhanced transformation matrix is an important prerequisite to develop the error estimation method. Adopting the basic concept of the error estimation method recently developed for the Craig–Bampton method, an error estimation method is developed for the AMLS method. Through various numerical examples, we demonstrate the accuracy of the proposed error estimation method and explore its computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.

A framework to validate and generate curved nodal high-order meshes on Computer-Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an *a posteriori* approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process. Copyright © 2015 John Wiley & Sons, Ltd.

The equations that govern Kirchhoff–Love plate theory are solved using quadratic Powell–Sabin B-splines and unstructured standard T-splines. Bézier extraction is exploited to make the formulation computationally efficient. Because quadratic Powell–Sabin B-splines result in -continuous shape functions, they are of sufficiently high continuity to capture Kirchhoff–Love plate theory when cast in a weak form. Unlike non-uniform rational B-splines (NURBS), which are commonly used in isogeometric analysis, Powell–Sabin B-splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T-splines can be modified such that they are -continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T-splines, Powell–Sabin B-splines and NURBS-to-NURPS (non-uniform rational Powell–Sabin B-splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plate. Copyright © 2015 John Wiley & Sons, Ltd.

The paper complements and extends the previous works on partitioned explicit wave propagation analysis methods, which were presented for discontinuous wave propagation problems in solids. An efficient implementation of the partitioned explicit wave propagation analysis methods is introduced. The present implementation achieves about 25% overall computational effort compared with the previous implementation with the same accuracy. The present algorithm tracks, with different integration time step sizes in accordance with their different wave speeds, the propagation fronts of longitudinal and shear waves. This is accomplished by integrating separately the element-by-element partitioned longitud inal and shear equations of motion. The state vectors (displacements, velocity and accelerations) of the longitudinal and shear components are reconciled at the end of each time step. The reconciliation procedure does not require any system parameters such as material properties, density, unlike conventional artificial viscosity methods. Numerical examples are presented as applied to linear and non-linear wave propagation problems, which demonstrate high-fidelity wavefront tracking ability of the present method, and compared with existing conventional wave propagation analysis methods. Copyright © 2015 John Wiley & Sons, Ltd.

The constantly rising demands on finite element simulations yield numerical models with increasing number of degrees-of-freedom. Due to nonlinearity, be it in the material model or of geometrical nature, the computational effort increases even further. For these reasons, it is today still not possible to run such complex simulations in real time parallel to, for example, an experiment or an application. Model reduction techniques such as the proper orthogonal decomposition method have been developed to reduce the computational effort while maintaining high accuracy. Nonetheless, this approach shows a limited reduction in computational time for nonlinear problems. Therefore, the aim of this paper is to overcome this limitation by using an additional empirical interpolation. The concept of the so-called discrete empirical interpolation method is translated to problems of solid mechanics with soft nonlinear elasticity and large deformations. The key point of the presented method is a further reduction of the nonlinear term by an empirical interpolation based on a small number of interpolation indices. The method is implemented into the finite element method in two different ways, and it is extended by using different solution strategies including a numerical as well as a quasi-Newton tangent. The new method is successfully applied to two numerical examples concerning hyperelastic as well as viscoelastic material behavior. Using the extended discrete empirical interpolation method combined with a quasi-Newton tangent enables reductions in computational time of factor 10 with respect to the proper orthogonal decomposition method without empirical interpolation. Negligibly, orders of error can be reached. Copyright © 2015 John Wiley & Sons, Ltd.

The investigation aims to formulate ground-structure based topology optimization approach by using a higher-order beam theory suitable for thin-walled box beam structures. While earlier studies use the Timoshenko or Euler beams to form a ground-structure, they are not suitable for a structure consisting of thin-walled closed beams. The higher-order beam theory takes into an additional account sectional deformations of a thin-walled box beam such as warping and distortion. Therefore, a method to connect ground beams at a joint and a technique to represent different joint connectivity states should be investigated for streamlined topology optimization. Several numerical case studies involving different loading and boundary conditions are considered to show the effectiveness of employing a higher-order beam theory for the ground-structure based topology optimization of thin-walled box beam structures. Through the numerical results, this work shows significant difference between optimized beam layouts based on the Timoshenko beam theory and those based on a more accurate higher-order beam theory for a structure consisting of thin-walled box beams. Copyright © 2015 John Wiley & Sons, Ltd.

The material point method is well suited for large-deformation problems in solid mechanics but requires modification to avoid cell-crossing errors as well as extension instabilities that lead to numerical (nonphysical) fracture. A promising solution is convected particle domain interpolation (CPDI), in which the integration domain used to map data between particles and the background grid deforms with the particle, based on the material deformation gradient. While eliminating the extension instability can be a benefit, it is often desirable to allow material separation to avoid nonphysical stretching. Additionally, large stretches in material points can complicate parallel implementation of CPDI if a single particle domain spans multiple computational patches. A straightforward modification to the CPDI algorithm allows a user-specified scaling of the particle integration domain to control the numerical fracture response, which facilitates parallelization. Combined with particle splitting, the method can accommodate materials with arbitrarily large failure strains. Used with a smeared damage/softening model, this approach will prevent nonphysical numerical fracture in situations where the material should remain intact, but the effect of a single velocity field on localization may still produce errors in the post-failure response. Details are given for both 2-D and 3-D implementations of the scaling algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, an anisotropic material model based on a non-associated flow rule and nonlinear mixed isotropic-kinematic hardening is developed. The quadratic Hill48 yield criterion is considered in the non-associated model for both yield function and plastic potential to account for anisotropic behavior. The developed model is integrated based on fully implicit backward Euler's method. The resulting problem is reduced to only two simple scalar equations. The consistent local tangent modulus is obtained by exact linearization of the algorithm. All numerical development was implemented into user-defined material subroutine for the commercial finite element code ABAQUS/Standard. The performance of the present algorithm is demonstrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

A new and efficient two-level, non-overlapping domain decomposition (DD) method is developed for the Helmholtz equation in the two Lagrange multiplier framework. The transmission conditions are designed by utilizing perfectly matched discrete layers (PMDLs), which are a more accurate representation of the exterior Dirichlet-to-Neumann map than the polynomial approximations used in the optimized Schwarz method. Another important ingredient affecting the convergence of a DD method, namely, the coarse space augmentation, is also revisited. Specifically, the widely successful approach based on plane waves is modified to that based on interface waves, defined directly on the subdomain boundaries, hence ensuring linear independence and facilitating the estimation of the optimal size for the coarse problem. The effectiveness of both PMDL-based transmission conditions and interface-wave-based coarse space augmentation is illustrated with an array of numerical experiments that include comprehensive scalability studies with respect to frequency, mesh size and the number of subdomains. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a lattice Boltzmann model for simulating linear elastic Lame equation is proposed. Differently from the classic lattice Boltzmann models, this lattice Boltzmann model is based on displacement distribution function in lattice Boltzmann equation. By using the technique of the higher-order moments of equilibrium distribution functions and a series of partial differential equations in different time scales, we obtain the Lame equation with fourth-order truncation errors. Based on this model, some problems with small deflection are simulated. The comparisons between the numerical results and the analytical solutions are given in detail. The numerical examples show that the lattice Boltzmann model can be used to solve problems of the linear elastic displacement field with small deflection. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we consider some potential formulations of electrostatic as well as time-harmonic eddy current problems with voltage or current excitation sources. The well-posedness of each formulation is first established. Then, the reliability of the corresponding residual-based a posteriori estimators is derived in the context of the finite element method approximation. Finally, the implementation in an industrial code is performed, and the obtained theoretical results are illustrated on an academic and on an industrial benchmark. Copyright © 2015 John Wiley & Sons, Ltd.

A three-dimensional surface adhesive contact formulation is proposed to simulate macroscale adhesive contact interaction characterized by the van der Waals interaction between arbitrarily shaped deformable continua under finite deformation. The proposed adhesive contact formulation uses a double-layer surface integral to replace the conventional double volume integration to compute the adhesive contact force vector. Considering nonlinear finite deformation, we have derived the surface stress tensor and the corresponding tangent stiffness matrix in a Galerkin weak formulation. With the surface stress formulation, the adhesive contact problems are solved in the framework of nonlinear continuum mechanics by using the standard Lagrange finite element method. Surface stress tensors are formulated for both interacting bodies. Numerical examples show that the proposed surface contact algorithm is accurate, efficient, and reliable for three-dimensional adhesive contact problems of large deformations for both quasi-static and dynamic simulations. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we analyze discontinuous finite volume methods for the stationary Stokes–Darcy problem that models coupled fluid flow and porous media flow. The discontinuous finite volume methods are combinations of finite volume method and discontinuous Galerkin method with three interior penalty types (incomplete symmetric, nonsymmetric, and symmetric), briefly, using discontinuous functions as trial functions in the finite volume method. Optimal error estimates in broken *H*^{1} norm are obtained for the three discontinuous finite volume methods. Optimal error estimates in the standard *L*^{2} norm are derived for the symmetric interior penalty discontinuous finite volume method. Numerical experiments are presented to confirm the theoretical results with non-matching meshes across the common interface of Stokes region and Darcy region. Copyright © 2015 John Wiley & Sons, Ltd.

The wave finite element (WFE) method is used for assessing the harmonic response of coupled mechanical systems that involve one-dimensional periodic structures and coupling elastic junctions. The periodic structures under concern are composed of complex heterogeneous substructures like those encountered in real engineering applications. A strategy is proposed that uses the concept of numerical wave modes to express the dynamic stiffness matrix (DSM), or the receptance matrix (RM), of each periodic structure. Also, the Craig–Bampton (CB) method is used to model each coupling junction by means of static modes and fixed-interface modes. An efficient WFE-based criterion is considered to select the junction modes that are of primary importance. The consideration of several periodic structures and coupling junctions is achieved through classic finite element (FE) assembly procedures, or domain decomposition techniques. Numerical experiments are carried out to highlight the relevance of the WFE-based DSM and RM approaches in terms of accuracy and computational savings, in comparison with the conventional FE and CB methods. The following test cases are considered: a 2D frame structure under plane stresses and a 3D aircraft fuselage-like structure involving stiffened cylindrical shells. Copyright © 2015 John Wiley & Sons, Ltd.

A new dual reciprocity-type approach to approximating the solution of non-homogeneous hyperbolic boundary value problems is presented in this paper. Typical variants of the dual reciprocity method obtain approximate particular solutions of boundary value problems in two steps. In the first step, the source function is approximated, typically using radial basis, trigonometric or polynomial functions. In the second step, the particular solution is obtained by analytically solving the non-homogeneous equation having the *approximation* of the source function as the non-homogeneous term. However, the particular solution trial functions obtained in this way typically have complicated expressions and, in the case of hyperbolic problems, points of singularity. Conversely, the method presented here uses the same trial functions for both source function and particular solution approximations. These functions have simple expressions and need not be singular, unless a singular particular solution is physically justified. The approximation is shown to be highly convergent and robust to mesh distortion.

Any boundary method can be used to approximate the complementary solution of the boundary value problem, once its particular solution is known. The option here is to use hybrid-Trefftz finite elements for this purpose. This option secures a domain integral-free formulation and endorses the use of super-sized finite elements as the (hierarchical) Trefftz bases contain relevant physical information on the modeled problem. Copyright © 2015 John Wiley & Sons, Ltd.

Goal-oriented error estimation allows to refine meshes in space and time with respect to arbitrary quantities. The required dual problems that need to be solved usually require weak formulations and the Galerkin method in space and time to be established. Unfortunately, this does not obviously leads to structures of standard finite element implementations for solid mechanics. These are characterized by a combination of variables at nodes (e.g. displacements) and at integration points (e.g. internal variables) and are solved with a two-level Newton method because of local uncoupled and global coupled equations. Therefore, we propose an approach to approximate the dual problem while maintaining these structures. The primal and the dual problems are derived from a multifield formulation. Discretization in time and space with appropriate shape functions and rearrangement yields the desired result. Details on practical implementation as well as applications to elasto-plasticity are given. Numerical examples demonstrate the effectiveness of the procedure. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, the extended finite element method (X-FEM) formulation for the modeling of arbitrary crack propagation in coupled shell/solid structures is developed based on the large deformation continuum-based (CB) shell theory. The main features of the new method are as follows: (1) different kinematic equations are derived for different fibers in CB shell elements, including the fibers enriched by shifted jump function or crack tip functions and the fibers cut into two segments by the crack surface or connecting with solid elements. So the crack tip can locate inside the element, and the crack surface is not necessarily perpendicular to the middle surface. (2) The enhanced CB shell element is developed to realize the seamless transition of crack propagation between shell and solid structures. (3) A revised interaction integral is used to calculate the stress intensity factor (SIF) for shells, which avoids that the auxiliary fields for cracks in Mindlin–Reissner plates cannot satisfy exactly the equilibrium equations. Several numerical examples, including the calculation of SIF for the cracked plate under uniform bending and crack propagation between solid and shell structures are presented to demonstrate the performance of the developed method. Copyright © 2015 John Wiley & Sons, Ltd.

An effective mesh generation algorithm is proposed to construct mesh representations for arbitrary fractures in 3D rock masses. With the development of advanced imaging techniques, fractures in a rock mass can be clearly captured by a high-resolution 3D digital image but with a huge data set. To reduce the data size, corresponding mesh substitutes are required in both visualization and numerical analysis. Fractures in rocks are naturally complicated. They may meet at arbitrary angles at junctions, which could derive topological defects, geometric errors or local connectivity flaws on mesh models. A junction weight is proposed and applied to distinguish fracture junctions from surfaces by an adequate threshold. We take account of fracture junctions and generate an initial surface mesh by a simplified centroidal Voronoi diagram. To further repair the initial mesh, an innovative umbrella operation is designed and adopted to correct mesh topology structures and preserve junction geometry features. Constrained with the aforementioned surface mesh of fracture, a tetrahedral mesh is generated and substituted for the 3D image model to be involved in future numerical analysis. Finally, we take two fractured rock samples as application examples to demonstrate the usefulness and capability of the proposed meshing approach. Copyright © 2015 John Wiley & Sons, Ltd.

The paper deals with the description, development and validation of an equivalent FEM element assembly suitable for the simulation of very compliant knitted meshes, like those used in elastic coatings, deployable antennas, medical applications and similar. The assembly is based on a network of lumped springs able to reproduce the orthotropic behaviour of the mesh when stretched along two directions. The parameters of the model have been identified by experimental tests using a dedicated biaxial testing device. The effectiveness of the modelling technique has been validated under two test settings, providing in-plane or out-of-plane displacements. For deformations up to 50%, the differences observed between experiments and numerical results are bounded below 6%. Copyright © 2015 John Wiley & Sons, Ltd.

During machining processes, the work piece material is subjected to high deformation rates, increased temperature, large plastic deformations, damage evolution and fracture. In this context the Johnson-Cook failure model is often used even though it exhibits pathological mesh size dependence. To remove the mesh size sensitivity, a set of mesh objective damage models is proposed based on a local continuum damage formulation combined with the concept of a scalar damage phase field. The first model represents a mesh objective augmentation of the well-established element removal model, whereas the second one degrades the continuum stress in a smooth fashion. Plane strain plate and hat specimens are used in the finite element simulations, with the restriction to the temperature and rate independent cases. To investigate the influence of mesh distortion, a structured and an unstructured meshes were used for the respective specimen. For structured meshes, the results clearly show that the pathological mesh size sensitivity is removed for both models. When considering unstructured meshes, the mesh size sensitivity is more complex as revealed by the considered hat-specimen shear test. Nevertheless, the present work indicates that the proposed models can predict realistic ductile failure behaviors in a mesh objective fashion. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a method is proposed for modeling explosive-driven fragments as spherical particles with a point-particle approach. Lagrangian particles are coupled with a multimaterial Eulerian solver that uses a three-dimensional finite volume framework on unstructured grids. The Euler–Lagrange method provides a straightforward and inexpensive alternative to directly resolving particle surfaces or coupling with structural dynamics solvers. The importance of the drag and inviscid unsteady particle forces is shown through investigations of particles accelerated in shock tube experiments and in condensed phase explosive detonation. Numerical experiments are conducted to study the acceleration of isolated explosive-driven particles at various locations relative to the explosive surface. The point-particle method predicts fragment terminal velocities that are in good agreement with simulations where particles are fully resolved, while using a computational cell size that is eight times larger. It is determined that inviscid unsteady forces are dominating for particles sitting on, or embedded in, the explosive charge. The effect of explosive confinement, provided by multiple particles, is investigated through a numerical study with a cylindrical C4 charge. Decreasing particle spacing, until particles are touching, causes a 30–50% increase in particle terminal velocity and similar increase in gas impulse. Copyright © 2015 John Wiley & Sons, Ltd.

To be feasible for computationally intensive applications such as parametric studies, optimization, and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that tend to dramatically increase computational complexity. Although significant progress has been achieved in the development of computational approaches for the reduction of nonlinear computational mechanics models, addressing the issue of contact remains a major hurdle. To this effect, this paper introduces a projection-based model reduction approach for both static and dynamic contact problems. It features the application of a non-negative matrix factorization scheme to the construction of a positive reduced-order basis for the contact forces, and a greedy sampling algorithm coupled with an error indicator for achieving robustness with respect to model parameter variations. The proposed approach is successfully demonstrated for the reduction of several two-dimensional, simple, but representative contact and self contact computational models. Copyright © 2015 John Wiley & Sons, Ltd.

We propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate. Ltd.Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, details of an implementation of a numerical code for computing the Kohn–Sham equations are presented and discussed. A fully self-consistent method of solving the quantum many-body problem within the context of density functional theory using a real-space method based on finite element discretisation of realspace is considered. Various numerical issues are explored such as (i) initial mesh motion aimed at co-aligning ions and vertices; (ii) *a priori* and *a posteriori* optimization of the mesh based on Kelly's error estimate; (iii) the influence of the quadrature rule and variation of the polynomial degree of interpolation in the finite element discretisation on the resulting total energy. Additionally, (iv) explicit, implicit and Gaussian approaches to treat the ionic potential are compared. A quadrupole expansion is employed to provide boundary conditions for the Poisson problem. To exemplify the soundness of our method, accurate computations are performed for hydrogen, helium, lithium, carbon, oxygen, neon, the hydrogen molecule ion and the carbon-monoxide molecule. Our methods, algorithms and implementation are shown to be stable with respect to convergence of the total energy in a parallel computational environment. Copyright © 2015 John Wiley & Sons, Ltd.

Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin projection, which changes during nonlinear solving (online analysis). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems. This model order reduction is assisted by a secant formulation which is updated by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to accelerate convergence in the reduced space, and a tangent formulation when correction of the reduced space is needed. Furthermore, this research shows that this adaptive strategy permits correction of the reduced model at low cost and small error. Copyright © 2015 John Wiley & Sons, Ltd.

A nonlinear nodal-integrated meshfree Galerkin formulation based on recently proposed strain gradient stabilization (SGS) method is developed for large deformation analysis of elastoplastic solids. The SGS is derived from a decomposed smoothed displacement field and is introduced to the standard variational formulation through the penalty method for the inelastic analysis. The associated strain gradient matrix is assembled by a B-bar method for the volumetric locking control in elastoplastic materials. Each meshfree node contains two coinciding integration points for the integration of weak form by the direct nodal integration scheme. As a result, a nonlinear stabilized nodal integration method with dual nodal stress points is formulated, which is free from stabilization control parameters and integration cells for meshfree computation. In the context of extreme large deformation analysis, an adaptive anisotropic Lagrangian kernel approach is introduced to the nonlinear SGS formulation. The resultant Lagrangian formulation is constantly updated over a period of time on the new reference configuration to maintain the well-defined displacement gradients as well as strain gradients in the Lagrangian computation. Several numerical benchmarks are studied to demonstrate the effectiveness and accuracy of the proposed method in large deformation inelastic analyses. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, a partitioned scheme for the numerical simulation of the surface-coupled problem of a fluid interacting with a saturated porous medium (fluid-porous-media interaction) is proposed by adopting the method of localised Lagrange multipliers, which facilitates an automatic spatial partitioning of the problem and a parallel treatment of the interacting components, and allows for using tailored solvers optimised for each subproblem. Moreover, proceeding from the interaction between an incompressible bulk fluid with a saturated biphasic porous medium with intrinsically incompressible and inert constituents, the characteristics of the governing equations are scrutinised, and the various constraints within the subsystems are identified. Following this, the method of perturbed Lagrange multipliers is used to replace the constrained equation systems within each subdomain by unconstrained ones. Furthermore, considering the one-dimensional (1D) version of the equations, a stability analysis of the proposed solution method is performed, and the unconditional stability of the partitioned solution scheme is shown. Solving 1D and 2D numerical benchmark examples, the applicability of the proposed scheme is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.

A three-dimensional nonlocal multiscale discrete-continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information-passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete-continuum coupling method retains the simplicity and efficiency of a continuum-based finite element model, while circumventing mesh pathology in the post-bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single-scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.

A universal, practical, a priori, numerical procedure is presented by which to realistically bind the spectral condition number of the global stiffness matrix generated by the finite element least-squares method. The procedure is then applied to second and fourth-order problems in one and two dimensions to show that the condition of the global stiffness matrix thus generated is, in all instances, proportional to but the diameter of the element squared. Copyright © 2015 John Wiley & Sons, Ltd.

In transient finite element analysis, reducing the time-step size improves the accuracy of the solution. However, a lower bound to the time-step size exists, below which the solution may exhibit spatial oscillations at the initial stages of the analysis. This numerical ‘shock’ problem may lead to accumulated errors in coupled analyses. To satisfy the non-oscillatory criterion, a novel analytical approach is presented in this paper to obtain the time-step constraints using the *θ*-method for the transient coupled analysis, including both heat conduction–convection and coupled consolidation analyses. The expressions of the minimum time-step size for heat conduction–convection problems with both linear and quadratic elements reduce to those applicable to heat conduction problems if the effect of heat convection is not taken into account. For coupled consolidation analysis, time-step constraints are obtained for three different types of elements, and the one for composite elements matches that in the literature. Finally, recommendations on how to handle the numerical ‘shock’ issues are suggested. Copyright © 2015 John Wiley & Sons, Ltd.

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]]>In computational contact mechanics problems, local searching requires calculation of the closest point projection of a contactor point onto a given target segment. It is generally supposed that the contact boundary is locally described by a convex region. However, because this assumption is not valid for a general curved segment of a three-dimensional quadratic serendipity element, an iterative numerical procedure may not converge to the nearest local minimum. To this end, several unconstrained optimization methods are tested: the Newton–Raphson method, the least square projection, the sphere and torus approximation method, the steepest descent method, the Broyden method, the Broyden–Fletcher–Goldfarb–Shanno method, and the simplex method. The effectiveness and robustness of these methods are tested by means of a proposed benchmark problem. It is concluded that the Newton–Raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods, whereas the torus approximation method can be recommended for contact searching algorithms, which employ the Lagrange method or the augmented Lagrangian method. Copyright © 2015 John Wiley & Sons, Ltd.

Cohesive zone models are widely used to model interface debonding problems; however, these models engender some significant drawbacks, including the need for a conforming mesh to delimit the interfaces between different materials or components and that penalty or other constraint methods necessary to enforce initially perfect adhesion at interfaces degrade the critical time step for stability in explicit time integration. This article proposes a new technique based on the extended finite element method that alleviates these shortcomings by representing the transition from perfect interfacial adhesion to debonding by switching the enriched approximation basis functions from weakly discontinuous to strongly discontinuous. At this transition, the newly activated degrees of freedom are initialized to satisfy a point-wise consistency condition at the interface for both displacement and velocity. Analysis of the stable time step for one-dimensional elements with mass lumping is presented, which shows the increase of the stable time step compared with a cohesive zone model. Both one-dimensional and two-dimensional verification examples are presented, illustrating the potential of this new approach. Copyright © 2015 John Wiley & Sons, Ltd.

We present a hybrid variational-collocation, immersed, and fully-implicit formulation for fluid-structure interaction (FSI) using unstructured T-splines. In our immersed methodology, we define an Eulerian mesh on the whole computational domain and a Lagrangian mesh on the solid domain, which moves arbitrarily on top of the Eulerian mesh. Mathematically, the problem reduces to solving three equations, namely, the linear momentum balance, mass conservation, and a condition of kinematic compatibility between the Lagrangian displacement and the Eulerian velocity. We use a weighted residual approach for the linear momentum and mass conservation equations, but we discretize directly the strong form of the kinematic relation, deriving a hybrid variational-collocation method. We use T-splines for both the spatial discretization and the information transfer between the Eulerian mesh and the Lagrangian mesh. T-splines offer us two main advantages against non-uniform rational B-splines: they can be locally refined and they are unstructured. The generalized-*α* method is used for the time discretization. We validate our formulation with a common FSI benchmark problem achieving excellent agreement with the theoretical solution. An example involving a partially immersed solid is also solved. The numerical examples show how the use of T-junctions and extraordinary nodes results in an accurate, efficient, and flexible method. Copyright © 2015 John Wiley & Sons, Ltd.