In this paper a structure-preserving direct method for the optimal control of mechanical systems is developed. The new method accommodates a large class of one-step integrators for the underlying state equations. The state equations under consideration govern the motion of affine Hamiltonian control systems. If the optimal control problem has symmetry, associated generalized momentum maps are conserved along an optimal path. This is in accordance with an extension of Noether's theorem to the realm of optimal control problems. In the present work we focus on optimal control problems with rotational symmetries. The newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem. This is true for a variety of one-step integrators used for the discretization of the state equations. Examples are the one-step theta method, a partitioned variant of the theta method, and energy-momentum consistent integrators. Numerical investigations confirm the theoretical findings. This article is protected by copyright. All rights reserved.

A general method is proposed to couple two sub-regions analysed with finite element digital image correlation (FE-DIC) even when using a mechanical regularization (R-DIC). A Lagrange multiplier is introduced to stitch both displacements fields in order to recover continuity over the full region of interest. Another interface unknown is introduced to ensure, additionally, the equilibrium of the mechanical models used for regularization. As a first application, the method is used to perform a single measurement from images at two different resolutions. Secondly, the method is also extended to parallel computing in R-DIC. The problem is formulated at the interface and solved with GMRes. A dedicated preconditioner is proposed to significantly accelerate convergence. The resulting method is a good candidate for the analysis of large data-sets. This article is protected by copyright. All rights reserved.

The representation of structural boundaries is of significant importance for the applications of DEM in industry. In recent decade, triangle meshes are extensively used for representing structural boundaries. Structural boundaries of industrial objects are composed by regular shapes and irregular shapes in many occasions. A method for representing structural boundaries with regular shapes and irregular shapes has been developed by combining mathematical equations and triangle meshes for computational efficiency. When structural boundaries are represented by mathematical equations and triangle meshes, gaps or protuberances may exist at the connection boundaries between regular shapes and irregular shapes. For the exactness of representation of structural boundaries, gaps or protuberances are identified, expressed and treated successively, so that the geometrical shapes composed by regular shapes described with mathematical equations and irregular shapes described with triangle meshes can replace the original structural shapes. Two series of numerical tests have been conducted to verify this method. The results showed that this method can effectively represent the complicated structural boundaries containing regular shapes and irregular shapes, and greatly reduce the computational cost in the contact detection between particles and structural boundaries.

This paper proposes a most probable point (MPP)-based dimension reduction method (DRM) using the Hessian matrix called HeDRM to improve accuracy of reliability analysis in existing MPP-based DRM methods. Conventional MPP-based DRMs contain two types of errors: (1) error due to eliminating cross-terms of a performance function by using the univariate DRM, (2) error due to dependency of an axis direction after a rotational transformation. The proposed method minimizes the aforementioned errors by utilizing the Hessian matrix of a performance function. By performing an orthogonal transformation using the eigenvectors of the Hessian matrix, the cross-term effect of the performance function is minimized and the axis direction that results in the most accurate calculation is obtained because the Gaussian quadrature points for numerical integration are arranged along the eigenvector directions. In this way, the error incurred by exiting MPP-based DRMs can be reduced which leads to more accurate probability of failure estimation. In addition, this paper proposes to allocate the Gaussian quadrature points using the magnitude of the eigenvalues of the Hessian matrix. This allocation makes it possible to predetermine the number of function evaluations required to estimate the probability of failure accurately and efficiently.

Uncertain static plane stress analysis of continuous structure involving interval fields is investigated in this study. Unlike traditional interval analysis of discrete structure, the interval field is adopted to model the uncertainty, as well as the dependency between the physical locations and degrees of variability, of all interval system parameters presented in the continuous structures. By implementing the flexibility properties of some common structural elements, a new computational scheme is proposed to reformulate the uncertain static plane stress analysis with interval fields into standard mathematical programming problems. Consequently, feasible upper and lower bounds of structural responses can be effectively yet efficiently determined. In addition, the proposed method is adequate to deal with situations involving one- and two-dimensional interval fields, which enhances the pertinence of the proposed approach by incorporating both discrete and continuous structures. In addition, the proposed computational scheme is able to establish the realizations of the uncertain parameters causing the extreme structural responses at zero computational cost. The applicability and credibility of the established computational framework are rigorously justified by various numerical investigations.

Efficient algorithms are considered for the computation of a reduced-order model based on the proper orthogonal decomposition methodology for the solution of parameterized elliptic partial differential equations. The method relies on partitioning the parameter space into subdomains based on the properties of the solution space and then forming a reduced basis for each of the subdomains. This yields more efficient offline and online stages for the proper orthogonal decomposition method. We extend these ideas for inexpensive adjoint based a posteriori error estimation of both the expensive finite element method solutions and the reduced-order model solutions, for a single and multiple quantities of interest. Various numerical results indicate the efficacy of the approach. This article is protected by copyright. All rights reserved.

This paper explores advantages offered by the stochastic collocation method based on the Smolyak grids for the solution of differential equations with random inputs in the parameter space. We use sparse Smolyak grids and the Chebyshev polynomials to construct multi-dimensional basis and approximate decoupled stochastic differential equations via interpolation. Disjoint set of grid points and basis functions allow us to gain significant improvement to conventional Smolyak algorithm. Density function and statistical moments of the solution are obtained by means of quadrature rules if inputs are uncorrelated and uniformly distributed. Otherwise, the Monte Carlo analysis can run inexpensively using obtained sparse approximation. An adaptive technique to sample from a multi-variate density function using sparse grid is proposed to reduce the number of required sampling points. Global sensitivity analysis is viewed as an extension of the sparse interpolant construction and is performed by means of the Sobol' variance-based or the Kullback-Leibler entropy methods identifying the degree of contribution from the individual inputs as well as the cross terms. This article is protected by copyright. All rights reserved.

The paper presents the generalization of the modification of classical boundary integral equation (BIE) and obtaining parametric integral equation system (PIES) for 2D elastoplastic problems. The modification was made to obtain such equations for which numerical solving does not require application of finite or boundary elements. This was achieved through the use of curves and surfaces for modeling introduced at the stage of analytical modification of the classic BIE. For approximation of plastic strains the Lagrange polynomials with various number and arrangement of interpolation nodes were used. Reliability of the modification was verified on examples with analytical solutions. This article is protected by copyright. All rights reserved.

The node or edge based smoothed finite element method is extended to develop polyhedral elements that are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation makes the element formulation simple and straightforward. The resulting polyhedral elements are free from the excessive zero-energy modes, and yield a robust solution very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The smoothed finite element methods based polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. This article is protected by copyright. All rights reserved.

We present two multiscale approaches for fracture analysis of full scale femur. The two approaches are the reduced order homogenization (ROH) previously developed by the first author and his associates and a novel accelerated reduced order homogenization (AROH). The AROH is based on utilizing reduced order homogenization calibrated to limited experimental data as a training tool to calibrate a simpler, single-scale anisotropic damage model. For bone tissue orientation, we take advantage of so-called Wolff's law, which states that bone tissue orientation is well correlated with principal strain direction in a stance position. The meso-phase properties are identified by minimizing error between the overall cortical and trabecular bone properties resulting from the quantitative computer tomography (QCT) scans and those predicted by the two-scale homogenization. The overall elastic and inelastic properties of the cortical and trabecular bone microstructure are derived from bone density that can be estimated from the Hounsfield units (HU) which represent the measured grey levels in the QCT scans. For model validation, we conduct ROH and AROH simulations of full scale finite element model of femur created from the QCT and compare the simulation results with available experimental data.

This paper aims at accounting for the uncertainties due to material structure and surface topology of micro-beams in a stochastic multiscale model. For micro-resonators made of anisotropic polycrystalline materials, micro-scale uncertainties are due to the grain size, grain orientation, and to the surface profile. First, micro-scale realizations of stochastic volume elements (SVEs) are obtained based on experimental measurements. To account for the surface roughness, the SVEs are defined as a volume element having the same thickness as the MEMS, with a view to the use of a plate model at the structural scale. The uncertainties are then propagated up to an intermediate scale, the meso-scale, through a second-order homogenization procedure. From the meso-scale plate resultant material property realizations, a spatially correlated random field of the in plane, out of plane, and cross resultant material tensors can be characterized. Owing to this characterized random field, realizations of MEMS-scale problems can be defined on a plate finite element model. Samples of the macro-scale quantity of interest can then be computed by relying on a Monte-Carlo simulation procedure. As a case study, the resonance frequency of MEMS micro-beams is investigated for different uncertainty cases, such as grain preferred orientations and surface roughness effects. Copyright © 2016 John Wiley & Sons, Ltd.

We propose a highly effective approach using a novel adaptive methodology to perform topology optimization with polygonal meshes, called polytree meshes. Polytree is a hierarchical data structure based on the principle of recursive spatial decomposition of each polygonal element with *n* nodes into (*n* + 1) arbitrary new polygonal elements; enabling more efficient utilization of unstructured meshes and arbitrary design domains in topology optimization. In order to treat hanging nodes after each optimization loop, we define the Wachspress coordinate on a reference element and then utilize an affine map to obtain shape functions and their gradients on arbitrary polygons with *n* vertices and *m* hanging nodes, called side-nodes, as the polygonal element with (*n* + *m*) vertices. The polytree meshes do not only improve the boundary description quality of the optimal result, but also reduce the computational cost of optimization process in comparison with the use of uniformly fine meshes. Several numerical examples are investigated to show the high effectiveness of the proposed method. This article is protected by copyright. All rights reserved.

We present an efficient numerical method to solve for cyclic steady states of nonlinear electro-mechanical devices excited at resonance. Many electro-mechanical systems are designed to operate at resonance, where the ramp-up simulation to steady state is computationally very expensive – especially when low damping is present. The proposed method relies on a Newton-Krylov shooting scheme for the direct calculation of the cyclic steady state, as opposed to a naïve transient time-stepping from zero initial conditions. We use a recently developed high-order Eulerian-Lagrangian finite element method in combination with an energy-preserving dynamic contact algorithm in order to solve the coupled electro-mechanical boundary value problem. The nonlinear coupled equations are evolved by means of an operator split of the mechanical and electrical problem with an explicit as well as implicit approach. The presented benchmark examples include the first three fundamental modes of a vibrating nanotube, as well as a micro-electro-mechanical disk resonator in dynamic steady contact. For the examples discussed, we observe power law computational speed-ups of the form *S* = 0.6·*ξ*^{−0.8}, where *ξ* is the linear damping ratio of the corresponding resonance frequency. This article is protected by copyright. All rights reserved.

We apply a combination of the transient scaled boundary finite element method (SBFEM) and quadtree-based discretization to model dynamic problems at high frequencies. We demonstrate that the current formulation of the SBFEM for dynamics tends to require more degrees of freedom than a corresponding spectral element discretization when dealing with smooth problems on regular domains. Thus, we improve the efficiency of the SBFEM by proposing a novel approach to reduce the number of auxiliary variables for transient analyses. Based on this improved SBFEM, we present a modified meshing procedure, which creates a quadtree mesh purely based on the geometry and allows arbitrary sizes and orders of elements, as well as an arbitrary number of different materials. The discretization of each subdomain is created automatically based on material parameters and the highest frequency of interest. The transition between regions of different properties is straightforward when using the SBFEM. The proposed approach is applied to image-based analysis with a particular focus on geological models. This article is protected by copyright. All rights reserved.

The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool which allows the proper transmission of information between finite element meshes. Since the Lagrangian projection of results from one mesh to another is a dissipative method, a new conservative interpolation method has been developed. A series of constraints, such as the conservation of mass or energy, are applied to the interpolated arrays through Lagrange multipliers in an error minimization problem, so that the resulting array satisfies these physical properties while staying as close as possible to the original interpolated values in the *L*^{2} norm. Unlike other conservative interpolation methods which require a considerable effort in mesh generation and modification, the proposed formulation is mesh independent and is only based on the physical properties of the field being interpolated. Moreover, the performed corrections are neither coupled with the main calculation nor with the interpolation itself, for which reason the computational cost is very low. This article is protected by copyright. All rights reserved.

A new algorithm called recursive absolute nodal coordinate formulation algorithm (REC-ANCF) is presented for dynamic analysis of multi-flexible-body system including nonlinear large deformation. This method utilizes the absolute nodal coordinate formulation (ANCF) to describe flexible bodies, and establishes a kinematic and dynamic recursive relationship for the whole system based on the articulated-body algorithm (ABA). In the ordinary differential equations (ODEs) obtained by the REC-ANCF, a simple form of the system generalized Jacobian matrix and generalized mass matrix is obtained. Thus, a recursive forward dynamic solution is proposed to solve the ODEs one element by one element through an appropriate matrix manipulation. Utilizing the parent array to describe the topological structure, the REC-ANCF is suitable for generalized tree multibody systems. Besides, the cutting joint method is used in simple closed-loop systems to make sure the O(n) algorithm complexity of the REC-ANCF. Compared with common ANCF algorithms, the REC-ANCF has several advantages: the optimal algorithm complexity (O(n)) under limited processors, simple derivational process, no location or speed constraint violation problem, higher algorithm accuracy. The validity and efficiency of this method are verified by several numerical tests. This article is protected by copyright. All rights reserved.

The possibility of using free-slip conditions within the context of the Particle Finite Element Method (PFEM) is investigated. For high Reynolds number engineering applications in which tangential effects at the fluid-solid boundaries are not of primary interest, the use of free-slip conditions can alleviate the need for very fine boundary layer meshes. Two novel ways for the imposition of free-slip conditions in the framework of the PFEM are presented. The proposed approach emphasizes robustness and simplicity, while retaining a sufficient level of generality. These two methods are then tested in the case of dam break and sloshing problems, and their respective advantages and drawbacks are discussed. It is also shown how the use of free-slip conditions can indirectly improve mass conservation properties of the PFEM, even when coarse meshes are employed. This article is protected by copyright. All rights reserved.

An adaptive mesh refinement (AMR) technique is proposed for level set (LS) simulations of incompressible multiphase flows. The present AMR technique is implemented for 2D/3D unstructured meshes and extended to multi-level refinement. Smooth variation of the element size is guaranteed near the interface region with the use of multi-level refinement. A Courant-Friedrich-Lewy (CFL) condition for zone adaption frequency is newly introduced to obtain a mass-conservative solution of incompressible multiphase flows. Finite elements around the interface are dynamically refined using the classical element subdivision method. Accordingly, finite element method is employed to solve the problems governed by the incompressible Navier-Stokes equations, using the LS method for dynamically updated meshes. The accuracy of the adaptive solutions is found to be comparable to that of non-adaptive solutions only if a similar mesh resolution near the interface is provided. Because of the substantial reduction in the total number of nodes, the adaptive simulations with two-level refinement used to solve the incompressible Navier-Stokes equations with a free surface are about four times faster than the non-adaptive ones. Further, the overhead of the present AMR procedure is found to be very small, as compared to the total CPU time for an adaptive simulation. This article is protected by copyright. All rights reserved.

A Fast Multipole Boundary Element Method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three-dimensional space is presented in this paper. The Collocation method is used, and the Burton-Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Due to the application of the combined integral equation (CHBIE), the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton-Miller formulation of the BIE, an integration technique for arbitrary element order is applied. The Fast Multipole Method combined with an arbitrary order h-p mesh refinement strategy enables accurate computation of large-scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time. This article is protected by copyright. All rights reserved.

Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by the matrix structures, properties of the eigen-solutions, sizes of the problems, etc. This paper aims to remove those limitations and develop robust and universal NEP solvers for large-scale engineering applications. The novelty lies in two aspects. First, a rational interpolation approach (RIA) is proposed based on the Keldysh theorem for holomorphic matrix functions. Comparing with the existing contour integral approach, the RIA provides the possibility to select sampling points in more general regions and has advantages in improving the accuracy and reducing the computational cost. Second, a resolvent sampling scheme using the RIA is proposed to construct reliable search spaces for the Rayleigh-Ritz procedure, based on which a robust eigen-solver, called RSRR, is developed for solving general NEPs. The RSRR can be easily implemented and parallelized. The advantages of the RIA and the performance of the RSRR are demonstrated by a variety of benchmark and application examples. This article is protected by copyright. All rights reserved.

We propose the study of a posteriori error estimates for time–dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors, independent of the heuristically chosen enrichment functions. Two sets of numerical experiments are presented. First, the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined. Second, the estimate is used to predict the behaviour of the error where no exact solution is available. It also reflects the errors incurred in the poorly conditioned systems typically encountered in generalised finite element methods. Finally we study local error indicators in individual time steps and elements of the mesh. This creates a basis towards the adaptive selection and refinement of the enrichment functions. This article is protected by copyright. All rights reserved.

The quasicontinuum (QC) method is a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. While traditional QC methods thereby create interfaces between fully-resolved and coarse-grained regions, the recently introduced fully-nonlocal QC framework does not fundamentally differentiate between atomistic and coarsened domains. Adding adaptive refinement enables us to tie atomistic resolution to evolving regions of interest such as moving defects. However, model adaptivity is challenging because large particle motion is described based on a reference mesh (even in the atomistic regions). Unlike in the context of, e.g., finite element meshes, adaptivity here requires that (i) all vertices lie on a discrete point set (the atomic lattice), (ii) model refinement is performed locally and provides sufficient mesh quality, and (iii) Verlet neighborhood updates in the atomistic domain are performed against a Lagrangian mesh. With the suite of adaptivity tools outlined here, the nonlocal QC method is shown to bridge across scales from atomistics to the continuum in a truly seamless fashion, as illustrated for nanoindentation and void growth. This article is protected by copyright. All rights reserved.

The automatic generation of meshes for the Finite Element (FE) method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the particles selected in a general domain. This study advances a numerical strategy that blends the FE method with the Meshless Local Petrov-Galerkin (MLPG) technique in structural mechanics, with the aim at exploiting the most attractive features of each procedure. The idea relies on the use of FEs to compute a background solution that is locally improved by enriching the approximation space with the basis functions associated to a few meshless points, thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid. Adding the meshless particles only where needed avoids the cost of mesh refining, or even of re-meshing, without the prohibitive computational cost of a thoroughly meshfree approach. In the present implementation, an efficient integration strategy for the computation of the coefficients taking into account the mutual FE-MLPG interactions is introduced. Moreover, essential boundary conditions are enforced separately on both FEs and meshless particles, thus allowing for an overall accuracy improvement also when the enriched region is close to the domain boundary. Numerical examples in structural problems show that the proposed approach can significantly improve the solution accuracy at a local level, with no re-meshing effort and at a low computational cost. This article is protected by copyright. All rights reserved.

A new four-node quadrilateral membrane finite element with drilling rotational degree of freedom based on the enhanced assumed strain formulation is presented. A simple formulation is achieved by five incompatible modes that are added to the Allman-type interpolation. Furthermore, modified shape functions are used to improve the behaviour of distorted elements. Numerical results show that the proposed new element exhibits good numerical accuracy and improved performance, and in many cases superior to existing elements. In particular, Poisson's locking in nearly incompressible elasticity fades, and the element performs well when it becomes considerably distorted even when it takes almost triangular shape. This article is protected by copyright. All rights reserved.

We present two accurate and efficient numerical schemes for a phase field dendritic crystal growth model, which is derived from the variation of a free energy functional, consisting of a temperature dependent bulk potential and a conformational entropy with a gradient-dependent anisotropic coefficient. We introduce a novel ‘Invariant Energy Quadratization ’ approach to transform the free energy functional into a quadratic form by introducing new variables to substitute the nonlinear transformations. Based on the reformulated equivalent governing system, we develop a first and a second order semi-discretized scheme in time for the system, in which all nonlinear terms are treated semi-explicitly. The resulting semi-discretized equations consist of a linear elliptic equation system at each time step, where the coefficient matrix operator is positive definite and thus the semi-discrete system can be solved efficiently. We further prove that the proposed schemes are unconditionally energy stable. Convergence test together with 2D and 3D numerical simulations for dendritic crystal growth are presented after the semi-discrete schemes are fully discretized in space using the finite difference method to demonstrate the stability and the accuracy of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.

The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. It is not straightforward to apply the available artificial boundary conditions for continua to peridynamic modeling. We therefore develop peridynamic transmitting boundary conditions (PTBCs) for one-dimensional wave propagation. Differently from the previous method where the matching boundary condition is constructed for only one boundary material point, the PTBCs are established by considering the interaction and exchange of information between a group of boundary material points and another group of inner material points. The motion of the boundary material points is recursively constructed in terms of their locations, and is determined through matching the peridynamic dispersion relation. The effectiveness of the PTBCs is examined by reflection analyses, numerical tests, and numerical convergent conditions. Furthermore, two-way interfacial conditions are proposed. The PTBCs are then applied to simulations of wave propagation in a bar with a defect, a composite bar with interfaces, and a domain with a seismic source. All the analyses and applications demonstrate that the PTBCs can effectively remove undesired numerical reflections at artificial boundaries. The methodology may be applied to modeling of wave propagation by other nonlocal theories. This article is protected by copyright. All rights reserved.

In the present paper, we address the delicate balance between computational efficiency and level of detailing at the modelling of ductile fracture in thin-walled structures. To represent the fine scale nature of the ductile process, we propose a new XFEM based enrichment of the displacement field to allow for cracks tips that end or kink within an element. The idea is to refine the crack tip element locally in a way such that the macroscale node connectivity is unaltered. This allows for a better representation of the discontinuous kinematics without affecting the macroscale solution procedure, which would be a direct consequence of a regular mesh refinement. The method is first presented in a general 3D setting and thereafter it is specialised to shell theory for the modelling of crack propagation in thin-walled structures. The paper is concluded by a number of representative examples showing the accuracy of the method. We conclude that the ideas proposed in the paper enhance the current methodology for the analysis of ductile fracture of thin-walled large scale structures under high strain rates. This article is protected by copyright. All rights reserved.

We present a higher-order discretization scheme for the compressible Euler and Navier-Stokes equations with immersed boundaries. Our approach makes use of a Discontinuous Galerkin (DG) discretization in a domain that is implicitly defined by means of a level set function. The zero iso-contour of this level set function is considered as an additional domain boundary where we weakly enforce boundary conditions in the same manner as in boundary-fitted cells. In order to retain the full order of convergence of the scheme, it is crucial to perform volume and surface integrals in boundary cells with high accuracy. This is achieved using a linear moment-fitting strategy. Moreover, we apply a non-intrusive cell-agglomeration technique that averts problems with very small and ill-shaped cuts. The robustness, accuracy and convergence properties of the scheme are assessed in several two-dimensional test cases for the steady compressible Euler and Navier-Stokes equations. Approximation orders range from zero to four, even though the approach directly generalizes to even higher orders. In all test cases with a sufficiently smooth solution, the experimental order of convergence matches the expected rate for DG schemes. This article is protected by copyright. All rights reserved.

Dynamic fragmentation is a rapid and catastrophic failure of a material. During this process, the nucleation, propagation, branching and coalescence of cracks results in the formation of fragments. The numerical modeling of this phenomenon is challenging because it requires high-performance computational capabilities. For this purpose the finite-element method with dynamic insertion of cohesive elements was chosen. This paper describes the parallel implementation of its fundamental algorithms in the C++ open-source library Akantu. Moreover a numerical instability that can cause the loss of energy conservation and possible solutions to it are illustrated. Finally, the method is applied to the dynamic fragmentation of a hollow sphere subjected to uniform radial expansion. This article is protected by copyright. All rights reserved.

In nonlinear model order reduction, hyper reduction designates the process of approximating a projection-based reduced-order operator on a reduced mesh, using a numerical algorithm whose computational complexity scales with the small size of the Projection-based Reduced-Order Model (PROM). Usually, the reduced mesh is constructed by sampling the large-scale mesh associated with the high-dimensional model underlying the PROM. The sampling process itself is governed by the minimization of the size of the reduced mesh for which the hyper reduction method of interest delivers the desired accuracy for a chosen set of training reduced-order quantities. Because such a construction procedure is combinatorially hard, its key objective function is conveniently substituted with a convex approximation. Nevertheless, for large-scale meshes, the resulting mesh sampling procedure remains computationally intensive. In this paper, three different convex approximations that promote sparsity in the solution are considered for constructing reduced meshes that are suitable for hyper reduction, and paired with appropriate active set algorithms for solving the resulting minimization problems. These algorithms are equipped with carefully designed parallel computational kernels in order to accelerate the overall process of mesh sampling for hyper reduction, and therefore achieve practicality for realistic, large-scale, nonlinear structural dynamics problems. Conclusions are also offered as to what algorithm is most suitable for constructing a reduced mesh for the purpose of hyper reduction. This article is protected by copyright. All rights reserved.

We propose a method to couple Smoothed Particle Hydrodynamics (SPH) and Finite Elements (FEM) methods for non-linear transient fluid-structure interaction simulations by adopting different time-steps depending on the fluid or solid sub-domains. These developments were motivated by the need to simulate highly non-linear and sudden phenomena requiring the use of explicit time integrators on both sub-domains (Explicit Newmark for the solid and Runge-Kutta 2 for the fluid). However, due to critical time-step required for the stability of the explicit time-integrators in, it becomes important to be able to integrate each sub-domain with a different time-step while respecting the features that a previously developed mono time-step coupling algorithm offered. For this matter, a dual-Schur decomposition method originally proposed for structural dynamics was considered, allowing to couple time-integrators of the Newmark family with different time-steps with the use of Lagrange multipliers. This article is protected by copyright. All rights reserved.

A large amount of research in computational mechanics has biased toward atomistic simulations. This trend, on one hand, is due to the increased demand to perform computations in nano-scale and, on the other hand, is due to the rather simple applications of pairwise potentials in modeling the interactions between atoms of a given crystal. The Cauchy-Born hypothesis has been used effectively to model the behavior of crystals under different loading conditions, in which the comparison with molecular dynamics simulations presents desirable coincidence between the results. A number of research works have been devoted to the validity of CB hypothesis and its application in post-elastic limit. However, the range of application of CB hypothesis is limited and it remains questionable whether it is still applicable beyond the validity limit. In this paper, a multi-scale technique is developed for modeling of plastic deformations in nano-scale materials. The deformation gradient is decomposed into the plastic and elastic parts, i.e. F = F^{p}F^{e}. This decomposition is in contrast to the conventional decomposition, F = F^{e}F^{p}, generally encountered in continuum and crystal plasticity. It is shown that the former decomposition is more appropriate for the problem dealt within this work. Inspired by crystal plasticity, the plastic part is determined from the slip on potential slip systems. Based on the assumption that the CB hypothesis remains valid in the homogeneous deformation, the elastic deformation gradient resulting from the aforementioned decomposition is employed in conjunction with the CB hypothesis to update the state variables for FCC crystals. The assumption of homogeneity of elastic deformation gradient is justified by the fact that elastic deformations are considerably smaller than the plastic deformations. The computational algorithms are derived in details and numerical simulations are presented through several examples to demonstrate the capability of the proposed computational algorithm in modeling of Golden crystals under different loading conditions. This article is protected by copyright. All rights reserved.

We introduce a method to mesh the boundary Γ of a smooth, open domain in
immersed in a mesh of tetrahedra. The mesh follows by mapping a specific collection of triangular faces in the mesh to Γ. Two types of surface meshes follow: (a) a mesh that *exactly* meshes Γ, and (b) meshes that approximate Γ to any order, by interpolating the map over the selected faces; that is, an isoparametric approximation to Γ. The map we use to deform the faces is the closest point projection to Γ. We formulate conditions for the closest point projection to define a homeomorphism between each face and its image. These are conditions on some of the tetrahedra intersected by the boundary, and they essentially state that each such tetrahedron should (a) have a small enough diameter, and (b) have two of its dihedral angles be acute. We provide explicit upper bounds on the mesh size, and these can be computed on the fly.

We showcase the quality of the resulting meshes with several numerical examples. More importantly, *all* surfaces in these examples were meshed with a *single* background mesh. This is an important feature for problems in which the geometry evolves or changes, because it could be possible for the background mesh to never change as the geometry does. In this case, the background mesh would be a universal mesh for all these geometries. We expect the method introduced here to be the basis for the construction of universal meshes for domains in three dimensions. Copyright © 2016 John Wiley & Sons, Ltd.

For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE–BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE–BE method. Copyright © 2016 John Wiley & Sons, Ltd.

A computational method is developed for evaluating the plastic strain gradient hardening term within a crystal plasticity formulation. While such gradient terms reproduce the size effects exhibited in experiments, incorporating derivatives of the plastic strain yields a nonlocal constitutive model. Rather than applying mixed methods, we propose an alternative method whereby the plastic deformation gradient is variationally projected from the elemental integration points onto a smoothed nodal field. Crucially, the projection utilizes the mapping between Lie groups and algebras in order to preserve essential physical properties, such as orthogonality of the plastic rotation tensor. Following the projection, the plastic strain field is directly differentiated to yield the Nye tensor. Additionally, an augmentation scheme is introduced within the global Newton iteration loop such that the computed Nye tensor field is fed back into the stress update procedure. Effectively, this method results in a fully implicit evolution of the constitutive model within a traditional displacement-based formulation. An elemental projection method with explicit time integration of the plastic rotation tensor is compared as a reference. A series of numerical tests are performed for several element types in order to assess the robustness of the method, with emphasis placed upon polycrystalline domains and multi-axis loading. Copyright © 2016 John Wiley & Sons, Ltd.

Atomistic models, which are crucial for performing molecular dynamics simulations of carbon nanostructures, consist of virtual hexagonal meshes with defects properly distributed in the intersectional areas. Currently, atomistic models are created mostly by hand, which is a notably tedious and time-consuming process. In this paper, we develop a method that produces atomistic models automatically. Because a hexagonal mesh and triangulation represent dual graphs, our work focuses on the creation of proper triangulation. The edge lengths of the triangulation should be compatible with the lengths of the C–C bonds, and vertices with valences other than 6 (due to the defects in the hexagonal mesh) should be properly arranged around the boundaries of the different components of a carbon nanostructure. Two techniques play important roles in our method: (1) sphere packing is used to place the nodes for triangulation that produces nearly constant edge lengths of the triangles and (2) the movement and editing of defects is used to control the number and positions of the defects. We subsequently develop a computer program based on this method that can create models much easier and faster than the current handwork method, thereby reducing the operation time significantly. Copyright © 2016 John Wiley & Sons, Ltd.

This work focuses on providing accurate low-cost approximations of stochastic finite elements simulations in the framework of linear elasticity. In a previous work, an adaptive strategy was introduced as an improved Monte-Carlo method for multi-dimensional large stochastic problems. We provide here a complete analysis of the method including a new enhanced goal-oriented error estimator and estimates of CPU (computational processing unit) cost gain. Technical insights of these two topics are presented in details, and numerical examples show the interest of these new developments. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, an efficient local radial basis function collocation method (LRBFCM) is presented for computing the band structures of the two-dimensional (2D) solid/fluid and fluid/solid phononic crystals. Both systems of solid scatterers embedded in a fluid matrix (solid/fluid phononic crystals) and fluid scatterers embedded in a solid matrix (fluid/solid phononic crystals) are investigated. The solid–fluid interactions are taken into account by properly formulating and treating the continuity/equilibrium conditions on the solid–fluid interfaces, which require an accurate computation of the normal derivatives of the displacements and the pressure on the fluid–solid interfaces and the unit-cell boundaries. The developed LRBFCM for the mixed wave propagation problems in 2D solid/fluid and fluid/solid phononic crystals is validated by the corresponding results obtained by the finite element method (FEM). To the best knowledge of the authors, the present LRBFCM has yet not been applied to the band structure computations of 2D solid/fluid and fluid/solid phononic crystals. For different lattice forms, scatterers' shapes, acoustic impedance ratios, and material combinations (solid scatterers in fluid matrix or fluid scatterers in solid matrix), numerical results are presented and discussed to reveal the efficiency and the accuracy of the developed LRBFCM for calculating the band structures of 2D solid/fluid and fluid/solid phononic crystals. A comparison of the present numerical results with that of the FEM shows that the present LRBFCM is much more efficient than the FEM for the band structure computations of the considered 2D solid/fluid and fluid/solid phononic crystals. Copyright © 2016 John Wiley & Sons, Ltd.

This article is concerned with the identification of stiffness parameters for short fiber-reinforced plastic materials, produced by injection molding and modeled by an orientation averaged transversely isotropic material law. Experiments are carried out in the form of computer simulations for a representative volume element of the material. The goal is to robustly identify the parameters with the fewest number of representative volume element simulations and such that the macroscopic model response attains a minimal variance for arbitrary strains and fiber orientations. Our approach carries over to problems involving anisotropic viscosity, thermal expansion and conductivity, and structurally similar problems. Copyright © 2016 John Wiley & Sons, Ltd.

In isogeometric analysis, identical basis functions are used for geometrical representation and analysis. In this work, non-uniform rational basis splines basis functions are applied in an isoparametric approach. An isogeometric Reissner–Mindlin shell formulation for implicit dynamic calculations using the Galerkin method is presented. A consistent as well as a lumped matrix formulation is implemented. The suitability of the developed shell formulation for natural frequency analysis is demonstrated by a numerical example. In a second set of examples, transient problems of plane and curved geometries undergoing large deformations in combination with nonlinear material behavior are investigated. Via a zero-thickness stress algorithm for arbitrary material models, a *J*_{2}-plasticity constitutive law is implemented. In the numerical examples, the effectiveness, robustness, and superior accuracy of a continuous interpolation method of the shell director vector is compared with experimental results and alternative numerical approaches. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we model crack discontinuities in two-dimensional linear elastic continua using the extended finite element method without the need to partition an enriched element into a collection of triangles or quadrilaterals. For crack modeling in the extended finite element, the standard finite element approximation is enriched with a discontinuous function and the near-tip crack functions. Each element that is fully cut by the crack is decomposed into two simple (convex or nonconvex) polygons, whereas the element that contains the crack tip is treated as a nonconvex polygon. On using Euler's homogeneous function theorem and Stokes's theorem to numerically integrate homogeneous functions on convex and nonconvex polygons, the exact contributions to the stiffness matrix from discontinuous enriched basis functions are computed. For contributions to the stiffness matrix from weakly singular integrals (because of enrichment with asymptotic crack-tip functions), we only require a one-dimensional quadrature rule along the edges of a polygon. Hence, neither element-partitioning on either side of the crack discontinuity nor use of any cubature rule within an enriched element are needed. Structured finite element meshes consisting of rectangular elements, as well as unstructured triangular meshes, are used. We demonstrate the flexibility of the approach and its excellent accuracy in stress intensity factor computations for two-dimensional crack problems. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, a new discrete elements generation method based on geometry is proposed to fill geometric domains with particles (disks or spheres). By generating particles each one with a random radius or with a radius calculated from the iteration to ensure no overlaps exist between particles and identifying unstable particles and changing them to stable ones, a dense and stable packing can be created. A partitioning particle radius interval method and a particle stability inspection and improvement method are introduced to guarantee the algorithm's success and the stability of the particles. Some packings were created to evaluate the performances of the new method. The results showed that the algorithm was very efficient and was able to create isotropic packings of low porosities and large coordinate numbers. The partitioning particle radius interval method improved the generation efficiency significantly and increased the packing densities. Through the comparisons with several existing methods proposed recently, the method proposed in this work is found to be more efficient and can fill geometric domains with the lowest porosities. In addition, the stability of the particles is guaranteed and no complex triangular or tetrahedral mesh is required in particle generation, thereby making the new method simpler. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes an original method to simulate the electrical conduction in continuums with the Discrete Element Method (DEM). The proposed method is based on the graphs theory applied to electrical resistance network, where the resistance between two discrete elements is estimated through the notion of ‘transmission surface’ to assume the discrete domain as a continuous medium. In addition to the electrical conduction, the Joule heating of a DEM domain has also been developed to take full advantage of the electrical conduction. The proposed method has been implemented in the free DEM software named ‘GranOO’.

The numerical results were compared against analytical approaches when applicable, or against Finite Element Method if the geometries become more complex or in case of dynamic loadings. The results are found satisfactory with errors around 3*%* for the electrical conduction and Joule heating of reasonably complex domains and loading cases. When it comes to more complex domains, such as electrical constriction, whilst the results remain close to those obtained with reference solutions (around 6*%*), they highlight the importance of taking care about the domains discretization.

Finally, the proposed method is applied to detect cracks onset on a cylindrical rod torsion test to show how to take advantage of the proposed work. Copyright © 2016 John Wiley & Sons, Ltd.

This article presents a detailed study on the potential and limitations of performing higher-order multi-resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high-contrast topologies, a length-scale is applied on the solution using filter methods. The relations between stiffness overestimation, the analysis system, and the applied length-scale are examined, while a high-resolution topology is maintained. The computational cost associated with nested topology optimization is reduced significantly compared with the use of first-order finite elements. This reduction is caused by exploiting the decoupling of density and analysis mesh, and by condensing the higher-order modes out of the stiffness matrix. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents an alternative topology optimization method based on an efficient meshless smoothed particle hydrodynamics (SPH) algorithm. To currently calculate the objective compliance, the deficiencies in standard SPH method are eliminated by introducing corrective smoothed particle method and total Lagrangian formulation. The compliance is established relative to a designed density variable at each SPH particle which is updated by optimality criteria method. Topology optimization is realized by minimizing the compliance using a modified solid isotropic material with penalization approach. Some numerical examples of plane elastic structure are carried out and the results demonstrate the suitability and effectiveness of the proposed SPH method in the topology optimization problem. Copyright © 2016 John Wiley & Sons, Ltd.

An accurate and easy integration technique is desired for the meshless methods of weak form. As is well known, a sub-domain method is often used in computational mechanics. The conforming sub-domains, where the sub-domains are not separated nor overlapped each other, are often used, while the nonconforming sub-domains could be employed if needed. In the latter cases, the integrations of the sub-domains may be performed easily by choosing a simple configuration. And then, the meshless method with nonconforming sub-domains is considered one of the reasonable choices for computational mechanics without the troublesome integration. In this paper, we propose a new sub-domain meshless method. It is noted that, because the method can employ both the conforming and the nonconforming sub-domains, the integration for the weak form is necessarily accurate and easy by selecting the nonconforming sub-domains with simple configuration. The boundary value problems including the Poisson's equation and the Helmholtz's equation are analyzed by using the proposed method. The numerical solutions are compared with the exact solutions and the solutions of the collocation method, showing that the relative errors by using the proposed method are smaller than those by using the collocation method and that the proposed method possesses a good convergence. Copyright © 2016 John Wiley & Sons, Ltd.

Large-scale systems of nonlinear equations appear in many applications. In various applications, the solution of the nonlinear equations should also be in a certain interval. A typical application is a discretized system of reaction diffusion equations. It is well known that chemical species should be positive otherwise the solution is not physical and in general blow up occurs. Recently, a projected Newton method has been developed, which can be used to solve this type of problems. A drawback is that the projected Newton method is not globally convergent. This motivates us to develop a new feasible projected Newton–Krylov algorithm for solving a constrained system of nonlinear equations. Combined with a projected gradient direction, our feasible projected Newton–Krylov algorithm circumvents the non-descent drawback of search directions which appear in the classical projected Newton methods. Global and local superlinear convergence of our approach is established under some standard assumptions. Numerical experiments are used to illustrate that the new projected Newton method is globally convergent and is a significate complementarity for Newton–Krylov algorithms known in the literature. © 2016 The Authors. *International Journal for Numerical Methods in Engineering* Published by John Wiley & Sons Ltd.

In this paper, we develop a strategy that enables a consistent wave transfer when coupling mechanical models exhibiting various description scales under dynamic loading. Incompatibilities between concurrent models are addressed by a selective filtering based on the perfectly matched layer framework and involving a dedicated projection operator. This filtering, performed in the vicinity of the coupling interface, aims at avoiding spurious wave reflections by automatically killing part of the signal with wavelength range not compatible with the downstream (coarser scale) model while the relevant complementary part is transferred. Performances of the proposed approach are evaluated in details by conducting one-dimensional and two-dimensional numerical experiments. The definition of the projection operator, which is a key point of the method, is particularly tackled by analyzing and comparing several possible choices. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, a novel time marching procedure is presented in which adaptive time integration parameters are locally computed, allowing different spatial and temporal distributions. As a consequence, a more versatile technique arises, enabling an enhanced performance. The main features of the proposed technique are: (1) it is simple; (2) it has guaranteed stability; (3) it is an efficient non-iterative adaptive single-step procedure; (4) it provides enhanced accuracy; (5) it enables advanced controllable algorithmic dissipation in the higher modes; (6) it is truly self-starting; and (7) it is entirely automatic, requiring no input parameter from the user. The proposed technique is very complete, providing the main positive attributes that are requested from an effective time marching procedure. Numerical results are presented along the paper, illustrating the excellent performance of the method. Copyright © 2016 John Wiley & Sons, Ltd.

A numerical procedure for analysis of general laminated plates under transverse load is developed utilizing the Mindlin plate theory, the finite volume discretization, and a segregated solution algorithm. The force and moment balance equations with the laminate constitutive relations are written in the form of a generic transport equation. In order to obtain discrete counterparts of the governing equations, the plate is subdivided into N control volumes by a Cartesian numerical mesh. As a result, five sets of N linear equations with N unknowns are obtained and solved using the conjugate gradient method with preconditioning.

For the method validation, a number of test cases are designed to cover thick and thin laminated plates with aspect ratio (width to thickness) from 4 to 100. Simply supported orthotropic, symmetric cross-ply, and angle-ply laminated plates under uniform and sinusoidal pressure loads are solved, and results are compared with available analytical solutions. The shear correction factor of 5/6 is utilized throughout the procedure, which is consistent with test cases used in the reviewed literature. Comparisons of the finite volume method results for maximum deflections at the center of the plate and the Navier solutions obtained for aspect ratios 10, 20, and 100 shows a very good agreement. Copyright © 2016 John Wiley & Sons, Ltd.

We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen *et al*. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca *et al*. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt. © 2016 The Authors. *International Journal for Numerical Methods in Engineering* Published by John Wiley & Sons, Ltd.

Represented by the element free Galerkin method, the meshless methods based on the Galerkin variational procedure have made great progress in both research and application. Nevertheless, their shape functions free of the Kronecker delta property present great troubles in enforcing the essential boundary condition and the material continuity condition. The procedures based on the relaxed variational formulations, such as the Lagrange multiplier-based methods and the penalty method, strongly depend on the problem in study, the interpolation scheme, or the artificial parameters. Some techniques for this issue developed for a particular method are hard to extend to other meshless methods. Under the framework of partition of unity and strict Galerkin variational formulation, this study, taking Poisson's boundary value problem for instance, proposes a unified way to treat exactly both the material interface and the nonhomogeneous essential boundary as in the finite element analysis, which is fit for any partition of unity-based meshless methods. The solution of several typical examples suggests that compared with the Lagrange multiplier method and the penalty method, the proposed method can be always used safely to yield satisfactory results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the development of mesh-free models for the static analysis of smart laminated composite beams. The overall smart composite beam is composed of a laminated substrate composite beam and a piezoelectric layer attached partially or fully at the top surface of the substrate beam. The piezoelectric layer acts as the distributed actuator layer of the smart beam. A layer-wise displacement theory and an equivalent single-layer theory have been used to derive the models. Several cross-ply substrate beams are considered for presenting the numerical results. The responses of the smart composite beams computed by the present new mesh-free model based on the layer-wise displacement theory excellently match with those obtained by the exact solutions. The mesh-free model based on the equivalent single-layer theory cannot accurately compute the responses due to transverse actuation by the piezoelectric actuator. The models derived here suggest that the mesh-free method can be efficiently used for the numerical analysis of smart structures. Copyright © 2016 John Wiley & Sons, Ltd.

This work deals with the efficient time integration of mechanical systems with elastohydrodynamic (EHD) lubricated joints. Two novel approaches are presented. First, a projection function is used to formulate the well-known Swift–Stieber cavitation condition and the mass-conservative cavitation condition of Elrod as an unconstrained problem. Based on this formulation, the pressure variable from the EHD problem is added to the dynamic equations of a multi-body system in a monolithic manner so that cavitation is solved within a global iteration. Compared with a partitioned state-of-the-art formulation, where the pressure is solved locally in a nonlinear force element, this global search reduces simulation time.

Second, a Quasi-Newton method of DeGroote is applied during time integration to solve the nonlinear relation between pressure and deformation. Compared with a simplified Newton method, the calculation of the time-consuming parts of the Jacobian are avoided, and therefore, simulation time is reduced significantly, when the Jacobian is calculated numerically. Solution strategies with the Quasi-Newton method are presented for the partitioned formulation as well as for the new DAE formulations with projection function. Results are given for a simulation example of a rigid shaft in a flexible bearing. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, we use Nitsche's formulation to weakly enforce kinematic constraints at an embedded interface in Helmholtz problems. Allowing embedded interfaces in a mesh provides significant ease for discretization, especially when material interfaces have complex geometries. We provide analytical results that establish the well-posedness of Helmholtz variational problems and convergence of the corresponding finite element discretizations when Nitsche's method is used to enforce kinematic constraints. As in the analysis of conventional Helmholtz problems, we show that the inf-sup constant remains positive provided that the Nitsche's stabilization parameter is judiciously chosen. We then apply our formulation to several 2D plane-wave examples that confirm our analytical findings. Doing so, we demonstrate the asymptotic convergence of the proposed method and show that numerical results are in accordance with the theoretical analysis. Copyright © 2016 John Wiley & Sons, Ltd.

We present a framework to efficiently solve large deformation contact problems with nearly incompressible materials by implementing adaptive remeshing. Specifically, nodally integrated elements are employed to avoid mesh locking when linear triangular or tetrahedral elements are used to facilitate mesh re-generation. Solution variables in the bulk and on contact surfaces are transferred between meshes such that accuracy is maintained and re-equilibration on the new mesh is possible. In particular, the displacement transfer in the bulk is accomplished through a constrained least squares problem based on nodal integration, while the transfer of contact tractions relies on parallel transport. Finally, a residual-based error indicator is chosen to drive adaptive mesh refinement. The proposed strategies are applicable to both two-dimensional or three-dimensional analysis and are demonstrated to be robust by a number of numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

The computation of elastic continua is widely used in today's engineering practice, and finite element models yield a reasonable approximation of the physically observed behaviour. In contrast, the failure of materials due to overloading can be seen as a sequence of discontinuous effects finally leading to a system failure. Until now, it has not been possible to sufficiently predict this process with numerical simulations. It has recently been shown that discrete models like lattice spring models are a promising alternative to finite element models for computing the breakdown of materials because of static overstress and fatigue. In this paper, we will address one of the downsides of current lattice spring models, the need for a periodic mesh leading to a mesh-induced anisotropy of material failure in simulations. We will show how to derive irregular cells that still behave as part of a homogeneous continuum irrespectively of their shape and which should be able to eliminate mesh-induced anisotropy. In addition, no restraints concerning the material stiffness tensor are introduced, which allows the simulation of non-isotropic materials. Finally, we compare the elastic response of the presented model with present lattice spring models using mechanical systems with a known analytical stress field. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. Copyright © 2016 John Wiley & Sons, Ltd.

The treatments of heterogeneities and periodic boundary conditions are explored to properly perform isogeometric analysis (IGA) based on NURBS basis functions in solving homogenization problems for heterogeneous media with omni-directional periodicity and composite plates with in-plane periodicity. Because the treatment of the combination of different materials in IGA models is not trivial especially for periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most awkward, but important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex-hull property of IGA. The issue arises from the introduction of overlapped control points located at angular points in the heterogeneous unit cell, which must satisfy multiple point constraint (MPC) conditions associated with periodic boundary conditions (PBCs). Although two measures may be conceivable, we suggest the use of multiple patches along with double MPC that imposes PBCs and the continuity conditions between different patches simultaneously. Several numerical examples of numerical material and plate tests are presented to demonstrate the validity of the proposed strategy of IG modeling for IGHA. Copyright © 2016 John Wiley & Sons, Ltd.

The discrete element method, developed by Cundall and Strack, typically uses some variations of the central difference numerical integration scheme. However, like all explicit schemes, the scheme is only conditionally stable, with the stability determined by the size of the time-step. The current methods for estimating appropriate discrete element method time-steps are based on many assumptions; therefore, large factors of safety are usually applied to the time-step to ensure stability, which substantially increases the computational cost of a simulation. This work introduces a general framework for estimating critical time-steps for any planar rigid body subject to linear damping and forcing. A numerical investigation of how system damping, coupled with non-collinear impact, affects the critical time-step is also presented. It is shown that the critical time-step is proportional to
if a linear contact model is adopted, where *m* and *k* represent mass and stiffness, respectively. The term which multiplies this factor is a function of known physical parameters of the system. The stability of a system is independent of the initial conditions. Copyright © 2016 John Wiley & Sons, Ltd.

We present a novel methodology to effectively localize radial basis function approximation methods in three dimensions. The local scheme requires shape parameter-dependent functions that can be used to approximate gradients of scattered data and to solve partial differential operators. The optimum shape parameter is obtained from the highest gradient of interest, where a known analytical function, when boundary conditions are not present, or a shape parameter-free global approximation are used to educate the localized scheme. The later option is applicable to problems where the operator needs to be solved multiple times, like in time evolution or stochastic integration. Past shape parameter's optimizations, for two-dimensional domains, based on the condition number of the interpolant matrix, were unable to provide satisfactory approximations. The applicability of our method is illustrated in the context of an analytical expression interpolation and during a Ginzburg–Landau relaxation of a free energy functional. In general, the optimum shape parameter depends on geometry, node distribution, and density, whereas the approximation errors decrease as the node density and the local stencil size increase. The effective localization of radial basis functions motivates its use in moving boundary problems and accelerates solutions through sparse matrix solvers. Copyright © 2016 John Wiley & Sons, Ltd.

The research work extends the *scaled boundary finite element method* to non-deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random-field uncertainties. The aim is to blend the scaled boundary finite element method into the Galerkin spectral stochastic methods, which leads to a proficient procedure for handling the stress singularity problems and crack analysis. The Young's modulus of structures is considered to have random-field uncertainty resulting in the stochastic behaviour of responses. Mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses (displacement, strain, and stress) and stress intensity factors of cracked structures. The feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we present a solution framework for high-order discretizations of conjugate heat transfer problems on non-body-conforming meshes. The framework consists of and leverages recent developments in discontinuous Galerkin discretization, simplex cut-cell techniques, and anisotropic output-based adaptation. With the cut-cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the discontinuous Galerkin discretization automatically adjusts the mesh in each sub-domain and achieves high-order accuracy in outputs of interest. We demonstrate the solution framework through several multi-domained conjugate heat transfer problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be difficult to capture with user-generated meshes. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion coefficients. More precisely, in the context of linear elliptic diffusion problems in randomly packed particulate composites, we develop an approach to strictly bound the error in the expectation and second moment of quantities of interest, without ever solving the fine-scale, intractable stochastic problem. The most attractive feature of our approach is that the error bounds are computed without any integration of the fine-scale features. Our computations are purely macroscopic, deterministic and remain tractable even for small scale ratios. The second contribution of the paper is an alternative derivation of modelling error bounds through the Prager–Synge hypercircle theorem. We show that this approach allows us to fully characterise and optimally tighten the interval in which predicted quantities of interest are guaranteed to lie. We interpret our optimum result as an extension of Reuss–Voigt approaches, which are classically used to estimate the homogenised diffusion coefficients of composites, to the estimation of macroscopic engineering quantities of interest. Finally, we make use of these derivations to obtain an efficient procedure for multiscale model verification and adaptation. Copyright © 2016 John Wiley & Sons, Ltd.

We study the simultaneous analysis and design (SAND) formulation of the ‘classical’ topology optimization problem subject to linear constraints on material density variables. Based on a dual method in theory, and a primal-dual method in practice, we propose a separable and strictly convex quadratic Lagrange–Newton subproblem for use in sequential approximate optimization of the SAND-formulated classical topology design problem.

The SAND problem is characterized by a large number of nonlinear equality constraints (the equations of equilibrium) that are linearized in the approximate convex subproblems. The availability of cheap second-order information is exploited in a Lagrange–Newton sequential quadratic programming-like framework. In the spirit of efficient structural optimization methods, the quadratic terms are restricted to the diagonal of the Hessian matrix; the subproblems have minimal storage requirements, are easy to solve, and positive definiteness of the diagonal Hessian matrix is trivially enforced.

Theoretical considerations reveal that the dual statement of the proposed subproblem for SAND minimum compliance design agrees with the ever-popular optimality criterion method – which is a nested analysis and design formulation. This relates, in turn, to the known equivalence between rudimentary dual sequential approximate optimization algorithms based on reciprocal (and exponential) intervening variables and the optimality criterion method. Copyright © 2016 John Wiley & Sons, Ltd.

Nonlocal integral and/or gradient enhancements are widely used to resolve the mesh dependency issue with standard continuum damage models. However, it is reported that whereas the structural response is mesh independent, a spurious damage growth is observed. Accordingly, a class of modified nonlocal enhancements is developed in literature, where the interaction domain increases with damage. In this contribution, we adopt a contrary view that the interaction domain *decreases* with damage. This is motivated by the fact that the fracture of quasi-brittle materials typically starts as a diffuse network of microcracks, before localizing into a macroscopic crack. To ensure thermodynamics consistency, the micromorphic theory is adopted in the model development. The ensuing microforce balance resembles closely the Helmholtz expression in a conventional gradient damage model. The superior performance of the localizing gradient damage model is demonstrated through a one-dimensional problem, as well as mode I and II failure in plane deformation. For all three cases, a localized deformation band at material failure is obtained. Copyright © 2016 John Wiley & Sons, Ltd.

A reduced order model (ROM) is presented for the long-term calculation of subsurface oil/water flows. As in several previous ROMs in the field, the Newton iterations in the full model (FM) equations, which are implicit in time, are projected onto a set of modes obtained by applying proper orthogonal decomposition (POD) to a set of snapshots computed by the FM itself. The novelty of the present ROM is that the POD modes are (i) first calculated from snapshots computed by the FM in a short initial stage, and then (ii) updated on the fly along the simulation itself, using new sets of snapshots computed by the FM in even shorter additional runs. Thus, the POD modes adapt themselves to the local dynamics along the simulation, instead of being completely calculated at the outset, which requires a computationally expensive preprocess. This strategy is robust and computationally efficient, which is tested in 10- and 30-year simulations for a realistic reservoir model taken from the SAIGUP project. Copyright © 2016 John Wiley & Sons, Ltd.

This article presents a family of variational integrators from a continuous time point of view. A general procedure for deriving symplectic integration schemes preserving an energy-like quantity is shown, which is based on the principle of virtual work. The framework is extended to incorporate holonomic constraints without using additional regularization. In addition, it is related to well-known partitioned Runge–Kutta methods and to other variational integration schemes. As an example, a concrete integration scheme is derived for the planar pendulum using both polar and Cartesian coordinates. Copyright © 2016 John Wiley & Sons, Ltd.

We study the alternative ‘simultaneous analysis and design’ (SAND) formulation of the local stress-constrained and slope-constrained topology design problem. It is demonstrated that a standard trust-region Lagrange–Newton sequential quadratic programming-type algorithm—based, in this case, on strictly convex and separable approximate subproblems—may converge to singular optima of the local stress-constrained problem without having to resort to relaxation or perturbation techniques. Moreover, because of the negation of the sensitivity analyses—in SAND, the density and displacement variables are independent—and the immense sparsity of the SAND problem, solutions to large-scale problem instances may be obtained in a reasonable amount of computation time. Copyright © 2016 John Wiley & Sons, Ltd.

Finite element method (FEM) is a well-developed method to solve real-world problems that can be modeled with differential equations. As the available computational power increases, complex and large-size problems can be solved using FEM, which typically involves multiple degrees of freedom (DOF) per node, high order of elements, and an iterative solver requiring several sparse matrix-vector multiplication operations. In this work, a new storage scheme is proposed for sparse matrices arising from FEM simulations with multiple DOF per node. A sparse matrix-vector multiplication kernel and its variants using the proposed scheme are also given for CUDA-enabled GPUs. The proposed scheme and the kernels rely on the mesh connectivity data from FEM discretization and the number of DOF per node. The proposed kernel performance was evaluated on seven test matrices for double-precision floating point operations. The performance analysis showed that the proposed GPU kernel outperforms the ELLPACK (ELL) and CUSPARSE Hybrid (HYB) format GPU kernels by an average of 42% and 32%, respectively, on a Tesla K20c card. Copyright © 2016 John Wiley & Sons, Ltd.

The current article presents a Lagrangian cell-centred finite volume solution methodology for simulation of metal forming processes. Details are given of the mathematical model in updated Lagrangian form, where a hyperelastoplastic *J*_{2} constitutive relation has been employed. The cell-centred finite volume discretisation is described, where a modified discretised is proposed to alleviate erroneous hydrostatic pressure oscillations; an outline of the memory efficient segregated solution procedure is given. The accuracy and order of accuracy of the method are examined on a number of 2-D and 3-D elastoplastic benchmark test cases, where good agreement with available analytical and finite element solutions is achieved. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we develop a robust reduced-order modeling method, named algebraic dynamic condensation, which is based on the improved reduced system method. Using algebraic substructuring, the global mass and stiffness matrices are divided into many small submatrices without considering the physical domain, and substructures and interface boundary are defined in the algebraic perspective. The reduced model is then constructed using three additional procedures: substructural stiffness condensation, interface boundary reduction, and substructural inertial effect condensation. The formulation of the reduced model is simply expressed at a submatrix level without using a transformation matrix that induces huge computational cost. Through various numerical examples, the performance of the proposed method is demonstrated in terms of accuracy and computational cost. Copyright © 2016 John Wiley & Sons, Ltd.

This work proposes novel stability-preserving model order reduction approaches for vibro-acoustic finite element models. As most research in the past for these systems has focused on noise attenuation in the frequency-domain, stability-preserving properties were of low priority. However, as the interest for time-domain auralization and (model based) active noise control increases, stability-preserving model order reduction techniques are becoming indispensable. The original finite element models for vibro-acoustic simulation are already well established but require too much computational load for these applications. This work therefore proposes two new global approaches for the generation of stable reduced-order models. Based on proven conditions for stability preservation under one-sided projection, a reformulation of the displacement-fluid velocity potential (*u* − *ϕ*) formulation is proposed. In contrast to the regular formulation, the proposed approach leads to a new asymmetric structure for the system matrices which is proven to preserve stability under one-sided projection. The second approach starts from a displacement-pressure (*u* − *p*) description where the system level projection space is decoupled for the two domains, for which we also prove the preservation of stability. Two numerical validation cases are presented which demonstrate the inadequacy of straightforward model order reduction on typical vibro-acoustic models for time-domain simulation and compare the performance of the proposed approaches. Both proposed approaches effectively preserve the stability of the original system. Copyright © 2016 John Wiley & Sons, Ltd.

The strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision. Copyright © 2016 John Wiley & Sons, Ltd.

When geometric uncertainties arising from manufacturing errors are comparable with the characteristic length or the product responses are sensitive to such uncertainties, the products of deterministic design cannot perform robustly. This paper presents a new level set-based framework for robust shape and topology optimization against geometric uncertainties. We first propose a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors in conjunction with Karhunen–Loève (K–L) expansion. We then utilize polynomial chaos expansion to implement the stochastic response analysis. In this context, the mathematical formulation of the considered robust shape and topology optimization problem is developed, and the adjoint-variable shape sensitivity scheme is derived. An advantage of this method is that relatively large shape variations and even topological changes can be accounted for with desired accuracy and efficiency. Numerical examples are given to demonstrate the validity of the present formulation and numerical techniques. In particular, this method is justified by the observations in minimum compliance problems, where slender bars vanish when the manufacturing errors become comparable with the characteristic length of the structures. Copyright © 2016 John Wiley & Sons, Ltd.

Discretization-induced oscillations in the load–displacement curve are a well-known problem for simulations of cohesive crack growth with finite elements. The problem results from an insufficient resolution of the complex stress state within the cohesive zone ahead of the crack tip. This work demonstrates that the *hp*-version of the finite element method is ideally suited to resolve this complex and localized solution characteristic with high accuracy and low computational effort. To this end, we formulate a local and hierarchic mesh refinement scheme that follows *dynamically* the propagating crack tip. In this way, the usually applied *static* a priori mesh refinement along the complete potential crack path is avoided, which significantly reduces the size of the numerical problem. Studying systematically the influence of *h*-refinement, *p*-refinement, and *h**p*-refinement, we demonstrate why the suggested *h**p*-formulation allows to capture accurately the complex stress state at the crack front preventing artificial snap-through and snap-back effects. This allows to decrease significantly the number of degrees of freedom and the simulation runtime. Furthermore, we show that by combining this idea with the finite cell method, the crack propagation within complex domains can be simulated efficiently without resolving the geometry by the mesh. Copyright © 2016 John Wiley & Sons, Ltd.

The FFT-based homogenization method of Moulinec–Suquet has recently emerged as a powerful tool for computing the macroscopic response of complex microstructures for elastic and inelastic problems. In this work, we generalize the method to problems discretized by trilinear hexahedral elements on Cartesian grids and physically nonlinear elasticity problems. We present an implementation of the basic scheme that reduces the memory requirements by a factor of four and of the conjugate gradient scheme that reduces the storage necessary by a factor of nine compared with a naive implementation.

For benchmark problems in linear elasticity, the solver exhibits mesh- and contrast-independent convergence behavior and enables the computational homogenization of complex structures, for instance, arising from computed tomography computed tomography (CT) imaging techniques. There exist 3D microstructures involving pores and defects, for which the original FFT-based homogenization scheme does not converge. In contrast, for the proposed scheme, convergence is ensured. Also, the solution fields are devoid of the spurious oscillations and checkerboarding artifacts associated to conventional schemes. We demonstrate the power of the approach by computing the elasto-plastic response of a long-fiber reinforced thermoplastic material with 172 × 10^{6} (displacement) degrees of freedom. Copyright © 2016 John Wiley & Sons, Ltd.

This work introduces a semi-analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis. Copyright © 2016 John Wiley & Sons, Ltd.

We propose a new method to obtain contact forces under a non-smoothed contact problem between arbitrarily-shaped bodies which are discretized by finite element method. Contact forces are calculated by the specific contact algorithm between two particles of smoothed particle hydrodynamics, which is a meshfree method, and that are applied to each colliding body. This approach has advantages that accurate contact forces can be obtained within an accelerated collision without a jump problem in a discrete time increment. Also, this can be simply applied into any contact problems like a point-to-point, a point-to-line, and a point-to-surface contact for complex shaped and deformable bodies. In order to describe this method, an impulse based method, a unilateral contact method and smoothed particle hydrodynamics method are firstly introduced in this paper. Then, a procedure about the proposed method is handled in great detail. Finally, accuracy of the proposed method is verified by a conservation of momentum through three contact examples. Copyright © 2016 John Wiley & Sons, Ltd.

This paper considers stochastic hybrid stress quadrilateral finite element analysis of plane elasticity equations with stochastic Young's modulus and stochastic loads. Firstly, we apply Karhunen–Loève expansion to stochastic Young's modulus and stochastic loads so as to turn the original problem into a system containing a finite number of deterministic parameters. Then we deal with the stochastic field and the space field by *k*−version/*p*−version finite element methods and a hybrid stress quadrilateral finite element method, respectively. We derive a priori error estimates, which are uniform with respect to the Lamè constant *λ*∈(0,+*∞*). Finally, we provide some numerical results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral finite volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/]. In Lee, Gil and Bonet (2013), a first-order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system, leading to excellent behaviour in two-dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the deformation gradient tensor must be curl-free throughout the deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge–Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the hyperelastic-GLACE nodal scheme of Kluth and Després (2010) is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications. Copyright © 2016 John Wiley & Sons, Ltd.

This paper describes a novel methodology that combines smoothed discrete particle hydrodynamics (SDPH) and finite volume method (FVM) to enhance the effective performance in solving the problems of gas-particle multiphase flow. To describe the collision and fluctuation of particles, this method also increases a new parameter, namely, granular temperature, according to the kinetic theory of granular flow. The coupled framework of SDPH–FVM has been established, in which the drag force and pressure gradient act on the SDPH particles and the momentum sources of drag force are added back onto the FVM mesh. The proposed technique is a coupled discrete-continuum method based on the two-fluid model. To compute for the discrete phase, its SDPH is developed from smoothed particle hydrodynamics (SPH), in which the properties of SPH are redefined with some new physical quantities added into the traditional SPH parameters, so that it is more beneficial for SDPH in representing the particle characteristics. For the continuum phase, FVM is employed to discretize the continuum flow field on a stationary grid by capturing fluid characteristics. The coupled method exhibits strong efficiency and accuracy in several two-dimensional numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd.

We present an adaptive variant of the measure-theoretic approach for stochastic characterization of micromechanical properties based on the observations of quantities of interest at the coarse (macro) scale. The salient features of the proposed nonintrusive stochastic inverse solver are identification of a nearly optimal sampling domain using enhanced ant colony optimization algorithm for multiscale problems, incremental Latin-hypercube sampling method, adaptive discretization of the parameter and observation spaces, and adaptive selection of number of samples. A complete test data of the TORAY T700GC-12K-31E and epoxy #2510 material system from the National Institute for Aviation Research report is employed to characterize and validate the proposed adaptive nonintrusive stochastic inverse algorithm for various unnotched and open-hole laminates. Copyright © 2016 John Wiley & Sons, Ltd.

A new smoothed finite element method (S-FEM) with tetrahedral elements for finite strain analysis of nearly incompressible solids is proposed. The proposed method is basically a combination of the F-bar method and edge-based S-FEM with tetrahedral elements (ES-FEM-T4) and is named ‘F-barES-FEM-T4’. F-barES-FEM-T4 inherits the accuracy and shear locking-free property of ES-FEM-T4. At the same time, it also inherits the volumetric locking-free property of the F-bar method. The isovolumetric part of the deformation gradient (*F*^{iso}) is derived from the ** F** of ES-FEM-T4, whereas the volumetric part (

In this study, a new mean-strain 10-node tetrahedral element is developed using energy-sampling stabilization. The proposed 10-node tetrahedron is composed of several four-node linear tetrahedral elements, four tetrahedra in the corners and four tetrahedra that tile the central octahedron in three possible sets of four-node linear tetrahedra, corresponding to three different choices for the internal diagonal. The assumed strains are calculated from mean ‘basis function gradients.’ The energy-sampling technique introduced previously for removing zero-energy modes in the mean-strain hexahedron is adapted for the present element: the stabilization energy is evaluated on the four-corner tetrahedra. The proposed element naturally leads to a lumped-mass matrix and does not have unphysical low-energy vibration modes. For simplicity, we limit our developments to linear elasticity with compressible and nearly incompressible material. The numerical tests demonstrate that the present element performs well compared with the classical 10-node tetrahedral elements for shell and plate structures, and nearly incompressible materials. Copyright © 2016 John Wiley & Sons, Ltd.

Couple stress formulations have been given much attention lately because of the possibility to explain cases, when the classical theory of elasticity fails to describe adequately the mechanical behavior. Such cases may include size-dependent stiffness, high stress gradients, and the response of materials with microstructure. Here, a new mixed Lagrangian formulation is developed for elastodynamic response within consistent size-dependent skew-symmetric couple stress theory. With a specific choice of mixed variables, the formulation can be written with only C^{0} continuity requirements, without the need to introduce a Lagrange multiplier or penalty method. Furthermore, this formulation permits, for the first time, the determination of natural frequencies within the consistent couple stress theory. Details for the strong form of the equilibrium equations, constitutive model relations, boundary conditions, and the corresponding weak form are provided. In addition, the discrete forms are also discussed with two approaches for reducing variables. Several simple two-dimensional computational example problems are then examined, along with a brief investigation of the effect of couple stress on natural frequencies, which exhibit size-dependence for most, but not all, modes. Copyright © 2016 John Wiley & Sons, Ltd.

Contact and fracture in the material point method require grid-scale enrichment or partitioning of material into distinct velocity fields to allow for displacement or velocity discontinuities at a material interface. A new method is presented in which a kernel-based damage field is constructed from the particle data. The gradient of this field is used to dynamically repartition the material into contact pairs at each node. This approach avoids the need to construct and evolve explicit cracks or contact surfaces and is therefore well suited to problems involving complex 3-D fracture with crack branching and coalescence. A straightforward extension of this approach permits frictional ‘self-contact’ between surfaces that are initially part of a single velocity field, enabling more accurate simulation of granular flow, porous compaction, fragmentation, and comminution of brittle materials. Numerical simulations of self contact and dynamic crack propagation are presented to demonstrate the accuracy of the approach. Copyright © 2016 John Wiley & Sons, Ltd.

We present three new sets of *C*^{1} hierarchical high-order tensor-product bases for conforming finite elements. The first basis is a high-order extension of the Bogner–Fox–Schmit basis. The edge and face functions are constructed using a combination of cubic Hermite and Jacobi polynomials with *C*^{1} global continuity on the common edges of elements. The second basis uses the tensor product of fifth-order Hermite polynomials and high-order functions and achieves global *C*^{1} continuity for meshes of quadrilaterals and *C*^{2} continuity on the element vertices. The third basis for triangles is also constructed using the tensor product of one-dimensional functions defined in barycentric coordinates. It also has global *C*^{1} continuity on edges and *C*^{2} continuity on vertices. A patch test is applied to the three considered elements. Projection and plate problems with smooth fabricated solutions are solved, and the performance of the *h*- and *p*-refinements are evaluated by comparing the approximation errors in the *L*_{2}- and energy norms. A plate with singularity is then studied, and *h*- and *p*-refinements are analysed. Finally, a transient problem with implicit time integration is considered. The results show exponential convergence rates with increasing polynomial order for the triangular and quadrilateral meshes of non-distorted and distorted elements. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, a simple locking-free triangular plate element, labeled here as Mindlin-type triangular plate element with nine degrees of freedom (MTP9), is presented. The element employs an incompatible approximation with nine degrees of freedom (DOFs) independent of the nodes and the shape of the triangle to define the displacements *u*/*v*/*w*(which is similar to a general solid element) along the *x*/*y*/*z* axes. It is free of shear locking, has a proper rank, and provides stable solutions for thick and thin plates. Moreover, the paper provides a new way to develop simple and efficient locking-free thick–thin-plate/shell elements. A variety of numerical examples demonstrate the convergence, accuracy, and robustness of the present element MTP9. Copyright © 2016 John Wiley & Sons, Ltd.

The paper is concerned with the modeling of the planar motion of a horizontal sheet of metal in a rolling mill. Inhomogeneous velocity profiles, with which the material is generated at one roll stand and enters the next one, lead to the time evolution of the deformation of the metal strip. We propose a novel kinematic description in which the axial coordinate is an Eulerian one, while the transverse motion of the sheet is modeled in a Lagrangian framework. The material volume travels across a finite element mesh, whose boundaries are in contact with the roll stands.

The concise mathematical formulation of the method is different from the classical form of the arbitrary Lagrangian–Eulerian approach with a rate form of constitutive relations.

The undeformed state of the strip is incompatible owing to the varying time rate of the generation of material. We treat this phenomenon by introducing the notion of intrinsic strains, which are mathematically described using the multiplicative decomposition of the deformation gradient.

We currently present the approach for quasistatic simulations of in-plane elastoplastic deformations of the strip. A practically relevant problem with two strip segments and three roll stands is studied in a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for *h*-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.

The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands the resolution of small length scales. The current standard algorithm for its solution, alternate minimization, is robust but converges slowly and demands the solution of large, ill-conditioned linear subproblems. In this paper, we propose several advances in the numerical solution of this model that improve its computational efficiency. We reformulate alternate minimization as a nonlinear Gauss–Seidel iteration and employ over-relaxation to accelerate its convergence; we compose this accelerated alternate minimization with Newton's method, to further reduce the time to solution, and we formulate efficient preconditioners for the solution of the linear subproblems arising in both alternate minimization and in Newton's method. We investigate the improvements in efficiency on several examples from the literature; the new solver is five to six times faster on a majority of the test cases considered. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.

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]]>In this paper, 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.

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 the combination of smoothed finite element method in terms of accuracy as well as stability. Copyright © 2016 John Wiley & Sons, Ltd.

Fibrous soft biological tissues such as skin, ligaments, tendons, and arteries are non-homogeneous composite materials composed of fibers embedded in a ground substance. Cyclic tensile tests on these type of materials usually show a hysteretic stress–strain behavior in which strain rate dependence (viscoelasticity) and softening (Mullins' effect) play a coupled role. The main contribution of the present paper is to present unified variational approach to model both coupled phenomena: nonlinear viscoelasticity and Mullins-like softening behavior. The approach is labeled as variational because viscous-strain and damage internal variables are updated based on the minimization of a hyperelastic-like potential that takes a renewed value at each time step. Numerical examples explores (a) the versatility of the proposed model to account for the two described phenomena according to the chosen functions for the free-energy and dissipative potentials, (b) the ability of the time-integration scheme embedded in the incremental potential definition to allow for large time increments, and (c) the capability of the model to mimic experimentally obtained stress–strain cyclic curves of soft tissues. The model implementation on standard finite elements is also tested in which symmetric analytic tangent matrices are used as a natural consequence of the variational nature of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

A stochastic thermo-mechanical model for strength prediction of concrete is developed, based on the two-scale asymptotic expressions, which involves both the macroscale and the mesoscale of concrete materials. The mesoscale of concrete is characterized by a periodic layout of unit cells of matrix-aggregate composite materials, consisting of randomly distributed aggregate grains and cement matrix. The stochastic second-order and two-scale computational formulae are proposed in detail, and the maximum normal stress is assumed as the strength criterion for the aggregates, and the cement paste, in view of their brittle characteristics. Numerical results for the strength of concrete obtained from the proposed model are compared with those from known experiments. The comparison shows that the proposed method is validated for strength prediction of concrete. The proposed thermo-mechanical model is also employed to investigate the influence of different volume fraction of the aggregates on the strength of concrete. Copyright © 2016 John Wiley & Sons, Ltd.

Thin-walled structures, when compressed, are prone to buckling. To fully utilize the capabilities of such structures, the post-buckling response should be considered and optimized in the design process. This work presents a novel method for gradient-based design optimization of the post-buckling performance of structures. The post-buckling analysis is based on Koiter's asymptotic method. To perform gradient-based optimization, the design sensitivities of the Koiter factors are derived, and new design optimization formulations based on the Koiter factors are presented. The proposed optimization formulations are demonstrated on a composite square plate and a curved panel where the post-buckling stability is optimized. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents the first method that enables the fully automatic generation of triangular meshes suitable for the so-called non-uniform rational B-spline (NURBS)-enhanced finite element method (NEFEM). The meshes generated with the proposed approach account for the computer-aided design boundary representation of the domain given by NURBS curves. The characteristic element size is completely independent of the geometric complexity and of the presence of very small geometric features. The proposed strategy allows to circumvent the time-consuming process of de-featuring complex geometric models before a finite element mesh suitable for the analysis can be produced. A generalisation of the original definition of a NEFEM element is also proposed, enabling to treat more complicated elements with an edge defined by several NURBS curves or more than one edge defined by different NURBS. Three examples of increasing difficulty demonstrate the applicability of the proposed approach and illustrate the advantages compared with those of traditional finite element mesh generators. Finally, a simulation of an electromagnetic scattering problem is considered to show the applicability of the generated meshes for finite element analysis. ©2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.