A unified strategy for the higher-order accurate integration of implicitly defined geometries is proposed. The geometry is represented by a higher-order level-set function. The task is to either integrate on the zero-level set or in the sub-domains defined by the sign of the level-set function. In three dimensions, this is either an integration on a surface or inside a volume. Starting point is the identification and meshing of the zero-level set by means of higher-order interface elements. For the volume integration, special sub-elements are proposed where the element faces coincide with the identified interface elements on the zero-level set. Standard Gauss points are mapped onto the interface elements or into the volumetric sub-elements. The resulting integration points may, for example, be used in fictitious domain methods and extended finite element methods. For the case of hexahedral meshes, parts of the approach may also be seen as a higher-order marching cubes algorithm. This article is protected by copyright. All rights reserved.

A novel computational method for simulating fatigue-driven mixed mode delamination cracks in laminated structures under cyclic loading is presented. The proposed fatigue method is based on linking a cohesive zone model for quasi-static crack growth and a ParisâĂŹ law like model described as a function of the energy release rate for the crack growth rate during cyclic loading. The J-integral has been applied to determine the energy release rate. Unlike other cohesive fatigue methods the proposed method depends only on quasi-static properties and ParisâĂŹ law parameters without relying on parameter fitting of any kind. The method has been implemented as a zero thickness 8-noded interface element for Abaqus and as a spring element for a simple finite element model in Matlab. The method has been validated in simulations of mode I, mode II and mixed mode crack loading for both self-similar and non-self-similar crack propagation. The method produces highly accurate results compared to currently available methods and is capable of simulating general mixed mode non-self-similar crack growth problems. This article is protected by copyright. All rights reserved.

The proposed spectral element method implementation is based on sparse matrix storage of local shape function derivatives calculated at Gauss-Lobatto-Legendre points. The algorithm utilizes two basic operations: multiplication of sparse matrix by vector and element by element vectors multiplication. Compute-intensive operations are performed for a part of equation of motion derived at the degree of freedom level of 3D isoparametric spectral elements. The assembly is performed at the force vector in such a way that atomic operations are minimized. This is achieved by a new mesh coloring technique The proposed parallel implementation of spectral element method on GPU is applied for the first time for Lamb wave simulations. It has been found that computation on multicore GPU is up to 14 times faster than on single CPU. This article is protected by copyright. All rights reserved.

A stabilized scheme is developed for mixed finite element methods for strongly coupled diffusion problems in solids capable of large deformations. Assumed enhanced strain techniques are employed to cure spurious oscillation patterns of low-order displacement/pressure mixed formulations in the incompressible limit for quadrilateral elements and brick elements. A study is presented which shows how hourglass instabilities resulting from geometrically nonlinear enhanced assumed strain methods have to be distinguished from pressure oscillation patterns due to the violation of the inf-sup condition. Moreover, an element formulation is proposed that provides stable results with respect to both types of instabilities. Comparisons are drawn between material models for incompressible solids of Mooney-Rivlin type and models for standard diffusion in solids with incompressible matrices such as polymeric gels. Representative numerical examples underline the ability of the proposed element formulation to cure instabilities of low-order mixed formulations. This article is protected by copyright. All rights reserved.

A new generalized damage model for quasi-incompressible hyperelasticity in a total Lagrangian finite strain framework is presented. A Kachanov-like reduction factor (1 ߚ *D*) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetric-isochoric split of the Helmholtz free energy. However, in the present work it has been implemented in an in-house finite element code for neo-Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three-dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature. This article is protected by copyright. All rights reserved.

A new numerical scheme, termed the seamless-domain method (SDM), is applied in a multiscale technique. The SDM requires only points and does not require a stiffness equation, mesh, grid, cell, or element. The SDM consists of two steps. The first step is a microscopic analysis of the local (small) simulation domain to obtain interpolation functions for discretizing governing equations. This allows an SDM solution to represent a heterogeneous material with microscopic constituents without homogenization. The second step is a macroscopic analysis of a seamless global (entire) domain that has no mesh and only coarse-grained points. The special functions obtained in the first step are used in interpolating the continuous dependent-variable distribution in the seamless global domain whose gradient is also continuous everywhere. The SDM would give a quite accurate solution for domains with strong boundary effects, anisotropic and heterogeneous materials, and isotropic homogeneous fields. Numerical examples of steady-state heat conduction fields are presented. For heterogeneous material, the SDM using only 117 points provided solutions as accurate as those of the traditional finite element method using 21665 nodes. Analysis of an isotropic material verified the cost effectiveness of the SDM as in the analysis of heterogeneous material. This article is protected by copyright. All rights reserved.

This work presents the temporal-spatial (full) dispersion and stability analysis of plane square linear and biquadratic serendipity finite elements in explicit numerical solution of transient elastodynamic problems. Here the central difference method, as an explicit time integrator, is exploited. The paper complements and extends the previous paper on spatial/grid dispersion analysis of plane square biquadratic serendipity finite elements by Kolman *et al.* (IJNME, 2013). We report on a computational strategy for temporalspatial dispersion relationships, where eigenfrequencies from grid/spatial dispersion analysis are adjusted to comply with the time integration method. Besides that, an ‘optimal’ lumped mass matrix for the studied finite element types is proposed and investigated. Based on the temporal-spatial dispersion and stability analysis, relationships suggesting the ‘proper’ choice of mesh size and time step size from knowledge of the loading spectrum are presented. This article is protected by copyright. All rights reserved.

The dynamic behavior of two 3-D rectangular permeable cracks in a transversely isotropic piezoelectric material is investigated under an incident harmonic stress wave by using the generalized Almansi's theorem and the Schmidt method. The problem is formulated through double Fourier transform into three pairs of dual integral equations with the displacement jumps across the crack surfaces as the unknown variables. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the dynamic stress field and the dynamic electric displacement filed near the crack edges are obtained and the effects of the shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the stress and the electric intensity factors in a piezoelectric composite material are analyzed. This article is protected by copyright. All rights reserved.

In this article we propose to discretize the problem of linear elastic homogenization by finite differences on a staggered grid, and introduce fast and robust solvers. Our method shares some properties with the FFT-based homogenization technique of Moulinec and Suquet, which has received widespread attention recently due to its robustness and computational speed. These similarities include the use of FFT, and the resulting performing solvers. The staggered grid discretization however, offers three crucial improvements. Firstly, solutions obtained by our method are completely devoid of the spurious oscillations characterizing solutions obtained by Moulinec-Suquet's discretization. Secondly, the iteration numbers of our solvers are bounded independently of the grid size and the contrast. In particular, our solvers converge for three-dimensional porous structures, which cannot be handled by Moulinec-Suquet's method. Thirdly, the finite difference discretization allows for algorithmic variants with lower memory consumption. More precisely, it is possible to reduce the memory consumption of the Moulinec-Suquet algorithms by 50*%*. We underline the effectiveness and the applicability of our methods by several numerical experiments of industrial scale. This article is protected by copyright. All rights reserved.

This work compares sample-based polynomial surrogates, well-suited for moderately high-dimensional stochastic problems. In particular, generalized Polynomial Chaos in its sparse pseudospectral form and stochastic collocation methods based on both isotropic and dimension-adapted sparse grids are considered. Both classes of approximations are compared and an improved version of a stochastic collocation with dimension-adaptivity driven by global sensitivity analysis is proposed. The stochastic approximations efficiency is assessed on multi-variate test function and airfoil aerodynamics simulations. The latter study addresses the probabilistic characterization of global aerodynamic coefficients derived from viscous subsonic steady flow about a NACA0015 airfoil in the presence of geometrical and operational uncertainties with both simplified aerodynamics model and RANS simulation. Sparse pseudospectral and collocation approximations exhibit similar level of performance for isotropic sparse simulation ensembles. Computational savings and accuracy gain of the proposed adaptive stochastic collocation driven by Sobol' indices are patent but remain problem-dependent. This article is protected by copyright. All rights reserved.

We present a sweeping window method in elastodynamics for detection of multiple flaws embedded in a large structure. The key idea is to measure the elastic wave propagation generated by a dynamic load within a smaller sub-structural detecting window domain, given a sufficient number of sensors. Hence rather than solving the full structure, one solves a set of smaller dynamic problems quickly and efficiently. To this end, an explicit dynamic eXtended Finite Element Method (XFEM) with circular/elliptical void enrichments is implemented to model the propagation of elastic waves in the detecting window domain. To avoid wave reflections, we consider the window as an unbounded domain with the option of full-/semi-/quarter-infinite domains and employ a simple multi-dimensional absorbing boundary layer technique. A spatially varying Rayleigh damping is proposed to eliminate spurious wave reflections at the artificial model boundaries. In the process of flaw detection, two phases are proposed: (i) *pre-analysis*–identification of rough damage regions through a data-driven approach and (ii) *post-analysis*–identification of the true flaw parameters by a two-stage optimization technique. The ‘pre-analysis’ phase considers the information contained in the ‘pseudo’ healthy structure and the scattered wave signals providing an admissible initial guess for the optimization process. Then a two-stage optimization approach (the simplex method and a damped Gauss-Newton algorithm) is carried out in the ‘post-analysis’ phase for convergence to the true flaw parameters. A weighted sum of the least squares, of the residuals between the measured and simulated waves, is used to construct the objective function for optimization. Several benchmark examples are numerically illustrated to test the performance of the proposed sweeping methodology for detection of multiple flaws in an unbounded elastic domain. This article is protected by copyright. All rights reserved.

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

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

Various techniques are proposed for reproducing the elastic wave propagation in an unbounded medium such as the infinite elements, the absorbing boundary conditions or the perfect matched layers. Here, a simplified approach is adopted by considering absorbing layers characterized by the viscous Rayleigh matrix as studied by Semblat *et al* [?semblat_2010,] and Rajagopal *et al* [?Rajagopal_ntde_2012,]. Further improvements to this procedure are provided. First, we start by establishing the strong form for the elastic wave propagation in a medium characterized by the Rayleigh matrix. This strong form will be used for deriving optimal conditions for damping out in the most efficient way the incident waves while seeking to avoid the spurious reflected waves at the interface between the domain of interest and the Rayleigh damping layer. A procedure for designing the absorbing layer is proposed by targeting a performance criterion expressed in terms of logarithmic decrement of wave amplitude in the layer thickness. A multilayer strategy is proposed to improve the efficiency of the absorbing boundary layer. The GC method proposed by Combescure and Gravouil [?gravouil_combescure_ijnme_2001,] is used to carry out explicit/implicit co-computations, making interact in time an explicit time integration scheme for the domain of interest with an implicit time integration scheme for the absorbing boundary layer. Efficiency of this approach in term of accuracy and CPU time is shown in 1D and 2D elastic wave propagation problems. This article is protected by copyright. All rights reserved.

This paper presents a multilevel algorithm for balanced partitioning of unstructured grids. The grid is partitioned such that the number of interface elements is minimized and each partition contains an equal number of grid elements. The partition refinement of the proposed multilevel algorithm is based on iterative tabu search procedure. In iterative partition refinement algorithms, tie-breaking in selection of maximum gain vertices affects the performance considerably. A new tie-breaking strategy in the iterative tabu search algorithm is proposed that leads to improved partitioning quality. Numerical experiments are carried out on various unstructured grids in order to evaluate the performance of the proposed algorithm. The partition results are compared with those produced by the well-known partitioning package Metis and *k*-means clustering algorithm, and shown to be superior in terms of edge cut, partition balance, and partition connectivity. This article is protected by copyright. All rights reserved.

The paper proposes a mixed finite element model and experiments its capability in the analysis of plastic collapse Reissner-Mindlin plates. The model is based on simple assumptions for the unknown fields, ensuring that it is easy to formulate and implement. A composite triangular mesh is assumed over the domain. Within each triangular element the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing a subdivision of the element into three triangular regions. The plastic collapse analysis is formulated as Quadratic and Conic mathematical programming problem and is accomplished by an Interior Point algorithm which furnishes both the collapse multiplier and the collapse mechanism. A series of numerical experiments shows that the proposed model performs well in plastic analysis, where it takes advantage of the absence of locking phenomena and the possibility of simply describe discontinuities in the plastic deformation field within the element. This article is protected by copyright. All rights reserved.

The objective of the present paper is to develop a *C**P**E* formulation for the numerical solution of three-dimensional problems of general hyperelastic orthotropic materials under finite deformations with initially distorted element shapes. Generally speaking, the accuracy of the *C**P**E* depends on the constitutive coefficients of the strain energy function that controls the inhomogeneous deformations. In the present study, a new methodology for the determination of the constitutive coefficients is presented, which allows the *C**P**E* to model any elastic material including isotropic, orthotropic and anisotropic materials, and with initially distorted element geometry. A number of example problems are considered, which verify and compare the performance of the developed *C**P**E* with other 3D brick elements that exist in the commercial finite element package ABAQUS. These examples demonstrate that the developed *C**P**E* is accurate, robust, free of hourglass instabilities, and can be used for modeling both 3D and thin structures that undergo large deformations. This article is protected by copyright. All rights reserved.

Applications where the diffusive and advective time scales are of similar order give rise to advection–diffusion phenomena that are inconsistent with the predictions of parabolic Fickian diffusion models. Non-Fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in Fickian models. In this work, we implement a modified, frame-invariant form of Cattaneo's hyperbolic diffusion relation within a spacetime discontinuous Galerkin advection–diffusion model. An *h*-adaptive spacetime meshing procedure supports an asynchronous, patch-by-patch solution procedure with linear computational complexity in the number of spacetime elements. This localized solver enables the selective application of optimization algorithms in only those patches that require inequality constraints to ensure a non-negative concentration solution. In contrast to some previous methods, we do not modify the numerical fluxes to enforce non-negative concentrations. Thus, the element-wise conservation properties that are intrinsic to discontinuous Galerkin models are defined with respect to physically meaningful Riemann fluxes on the element boundaries. We present numerical examples that demonstrate the effectiveness of the proposed model, and we explore the distinct features of hyperbolic advection–diffusion response in subcritical and supercritical flows. This article is protected by copyright. All rights reserved.

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

The discrete nature of matter – typically recognised at the microscale – is usually replaced by a continuous model at the macroscale. However, the discrete model of solids can be adopted also at the macroscopic scale, still enabling the description of the main mechanical phenomena; furthermore the discrete approach, tailored to the scale of observation of interest, allows the multiscale study of solids. The paper presents a general computational particle method – whose particle interaction is modelled through force functionals, related to the nature of the material being analyzed (solid, granular or their interaction) – that represents a unified computational mechanical model suitable for a wide class of problems. This force interaction evaluation is also adopted for the boundary- and for the particle-particle contacts. Its allows to easily assess the dynamic response and failure of solids, granular or their interaction, avoiding the drawbacks of continuous approaches that typically require complex remeshing operations, stress field enrichment or the introduction of discontinuous displacement field for the solution of such problems. Some examples, aimed at demonstrating the versatility of the approach, are finally presented: in particular the failure of solids under impact and confined particles flows are simulated and the related results discussed. This article is protected by copyright. All rights reserved.

This paper proposes a relative new method called time-domain Galerkin method (TDGM) for investigating the structural dynamic load identification problems. Firstly, the shape functions are adopted to approximate three parameters, such as the dynamic load, kernel function response and measured structural response Secondly, defining a residual function could be expressed as the difference of the left side and right side of the convolution equation. Thirdly, to select an appropriate weighting function while making the integral with respect to parameter *t* of the residuals multiplied by a weighting function to be zero. Finally when the shape functions are chosen as the weighting function, it establishes the forward model called TDGM. Furthermore the regularization method could have effectiveness in solving the ill-posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load. Compared with the traditional Green kernel function method (GKFM), TDGM can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification. Three numerical examples are provided to demonstrate the correctness and advantages of TDGM. This article is protected by copyright. All rights reserved.

In this paper, a continuum membrane theory and its subsequent finite element approximation for the description of arbitrary shell-like nanostructures such as graphene-based nanostructures is presented. This is done by applying a multiscale approach where the continuum membrane is linked to the underlying atomistic lattice. This linkage is performed by the exponential generalization of the Cauchy-Born hypothesis, since the classical Cauchy-Born hypothesis is restricted to three-dimensional bulk structures and is thus not applicable to shell-like structures. However, the approximations of the exponential Cauchy-Born hypothesis published so far are limited to structures with a planar reference configuration. In this paper, we present an extended approximation, which does not require the reference configuration to be planar and is thus applicable to arbitrarily shaped shell-like nanostructures. A detailed elaboration of the related finite element implementation with important computational aspects is presented. Finally, the accuracy of the proposed method and its implementation is verified with several numerical examples. This article is protected by copyright. All rights reserved.

This paper proposed a rotation free thin shell formulation with nodal integration for elastic-static, free vibration and explicit dynamic analyses of structures using three-node triangular cells and linear interpolation functions. The formulation is based on the classic Kirchhoff plate theory, in which only three translational displacements are treated as the filed variables. Based on each node, the integration domains are further formed, where the generalized gradient smoothing technique (GST) and Green divergence theorem that can relax the continuity requirement for trial function are used to construct the curvature filed. With the aid of strain smoothing operation and tensor transformation rule, the smoothed strains in the integration domain can be finally expressed by constants. The principle of virtual work (PVW) is then used to establish the discretized system equations. The translational boundary conditions are imposed same as the practice of standard FEM, while the rotational boundary conditions are constrained in the process of constructing the smoothed curvature filed. To test the performance of the present formulation, several numerical examples, including both benchmark problems and practical engineering cases, are studied. The results demonstrate that the present method possesses better accuracy and higher efficiency for both static and dynamic problems.

In this work, we propose Runge-Kutta time integration schemes for the incompressible Navier-Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both velocities and pressures. The *segregated Runge-Kutta* methods are motivated as an implicit-explicit Runge-Kutta time integration of the projected Navier-Stokes system onto the discrete divergence-free space, and its re-statement in a velocity-pressure setting using a discrete pressure Poisson equation. We have analyzed the preservation of the discrete divergence constraint for segregated Runge-Kutta methods, and their relation (in their fully explicit version) with existing half-explicit methods. We have performed a detailed numerical experimentation for a wide set of schemes (from first to third order), including implicit and IMEX integration of viscous and convective terms, for incompressible laminar and turbulent flows. Further, segregated Runge-Kutta schemes with adaptive time stepping are proposed. This article is protected by copyright. All rights reserved.

We consider event-driven schemes for the simulation of nonseparable mechanical systems subject to holonomic unilateral constraints. Systems are modeled in discrete time using variational integrator (VI) theory, by which equations of motion follow from discrete variational principles. For smooth dynamics, VIs are known to exactly conserve a discrete symplectic form and a modified Hamiltonian function. The latter of these conservation laws can play a pivotal role in stabilizing the energy behavior of collision simulations. Previous efforts to leverage modified Hamiltonian conservation have been limited to integrators using the Störmer-Verlet method on separable, nonsmooth Hamiltonian mechanical systems. We generalize the existing approach to the family of all VIs applied to nonseparable, potentially nonconservative Lagrangian mechanical systems. We examine the properties of the resulting integrators relative to other structured collision simulation methods in terms of conserved quantities, trajectory errors as a function of initial condition, and required computation time. Interestingly, we find that the modified collision Verlet algorithm (MCVA) using the Störmer-Verlet integrator defined as a composition method leads to the best accuracy. Although, relative to this method the VI-based generalized MCVA method offers computational savings when collisions are particularly sparse. This article is protected by copyright. All rights reserved.

This work proposes a method for statistical effect screening to identify design parameters of a numerical simulation that are influential to performance while simultaneously being robust to epistemic uncertainty introduced by calibration variables. Design parameters are controlled by the analyst, but the optimal design is often uncertain, while calibration variables are introduced by modeling choices. We argue that uncertainty introduced by design parameters and calibration variables should be treated differently, despite potential interactions between the two sets. Herein, a robustness criterion is embedded in our effect screening to guarantee the influence of design parameters, irrespective of values used for calibration variables. The Morris screening method is utilized to explore the design space, while robustness to uncertainty is quantified in the context of info-gap decision theory. The proposed method is applied to the NASA Multidisciplinary Uncertainty Quantification Challenge Problem, which is a black-box code for aeronautic flight guidance that requires 35 input parameters. The application demonstrates that a large number of variables can be handled without formulating simplifying assumptions about the potential coupling between calibration variables and design parameters. Due to the computational efficiency of the Morris screening method, we conclude that the analysis can be applied to even larger-dimensional problems.

A computational scheme is developed for sampling-based evaluation of a function whose inputs are statistically variable. After a general abstract framework is developed, it is applied to initialize and evolve the size and orientation of cracks within a finite domain, such as a finite element or similar subdomain. The finite element is presumed to be too large to explicitly track each of the potentially thousands (or even millions) of individual cracks in the domain. Accordingly, a novel binning scheme is developed that maps the crack data to nodes on a reference grid in probability space. The scheme, which is clearly generalizable to applications involving arbitrary numbers of random variables, is illustrated in the scope of planar deformations of a brittle material containing straight cracks. Assuming two random variables describe each crack, the cracks are assigned uniformly random orientations and non-uniformly random sizes. Their data are mapped to a computationally tractable number of nodes on a grid laid out in the unit square of probability space so that Gauss points on the grid may be used to define an equivalent subpopulation of the cracks. This significantly reduces the computational cost of evaluating ensemble effects of large evolving populations of random variables. This article is protected by copyright. All rights reserved.

A simultaneous iterative procedure for the Kron's component modal synthesis method is developed in this paper for fast calculating the modal parameters of a large-scale and/or complicated structure. To simultaneously improve the precision of all the concerned modal parameters, the modal transformation matrix is chosen as the iterative term. For a faster convergence rate, the reduced system matrices are consistent with the modal transformation matrix. With a mathematically proved consistency and reasonably justified convergence, the proposed method can provide highly accurate results after a few iterations. The implementation details are presented for reference together with some computational considerations. Compared with other methods for obtaining modal parameters, the proposed method has such merits as high computational efficiency and still in a substructuring scheme. Two numerical examples are provided to illustrate and validate the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

A variation of the extended finite element method for three-dimensional fracture mechanics is proposed. It utilizes a novel form of enrichment and point-wise and integral matching of displacements of the standard and enriched elements in order to achieve higher accuracy, optimal convergence rates, and improved conditioning for two-dimensional and three-dimensional crack problems. A bespoke benchmark problem is introduced to determine the method's accuracy in the general three-dimensional case where it is demonstrated that the proposed approach improves the accuracy and reduces the number of iterations required for the iterative solution of the resulting system of equations by 40% for moderately refined meshes and topological enrichment. Moreover, when a fixed enrichment volume is used, the number of iterations required grows at a rate which is reduced by a factor of 2 compared with standard extended finite element method, diminishing the number of iterations by almost one order of magnitude. Copyright © 2015 John Wiley & Sons, Ltd.

Energy harvesting devices are smart structures capable of converting the mechanical energy (generally, in the form of vibrations) that would be wasted otherwise in the environment into usable electrical energy. Laminated piezoelectric plate and shell structures have been largely used in the design of these devices because of their large generation areas. The design of energy harvesting devices is complex, and they can be efficiently designed by using topology optimization methods (TOM). In this work, the design of laminated piezocomposite energy harvesting devices has been studied using TOM. The energy harvesting performance is improved by maximizing the effective electric power generated by the piezoelectric material, measured at a coupled electric resistor, when subjected to a harmonic excitation. However, harmonic vibrations generate mechanical stress distribution that, depending on the frequency and the amplitude of vibration, may lead to piezoceramic failure. This study advocates using a global stress constraint, which accounts for different failure criteria for different types of materials (isotropic, piezoelectric, and orthotropic). Thus, the electric power is maximized by optimally distributing piezoelectric material, by choosing its polarization sign, and by properly choosing the fiber angles of composite materials to satisfy the global stress constraint. In the TOM formulation, the Piezoelectric Material with Penalization and Polarization material model is applied to distribute piezoelectric material and to choose its polarization sign, and the Discrete Material Optimization method is applied to optimize the composite fiber orientation. The finite element method is adopted to model the structure with a piezoelectric multilayered shell element. Numerical examples are presented to illustrate the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

A semi-continuous formulation is introduced for finding bases that minimise the error in a specific output functional of a reduced-order model. The formulation is advantageous in that it can be used with arbitrary reference data and can be easily applied to nonlinear models and functionals. A general description of the approach is given; then, explicit formulations are derived for the advection-diffusion and Burgers' equations. Numerical results are given for both linear and nonlinear functionals. These show substantial reductions in error when compared with POD modes, depending on the functional considered. The optimisation of bases for a reduced-order model using an approximated governing equation is also described, for which large increases in accuracy are obtained relative to POD modes. Copyright © 2015 John Wiley & Sons, Ltd.

This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we address shortcomings of the method of exponential basis functions by extending it to general linear and non-linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non-linear problems, they are converted to into a succession of linear ones using a Newton–Kantorovich approach. The generalized exponential basis functions (GEBF) method developed can be implemented with greater ease compared with exponential basis functions, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. We compare GEBF on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also, in a 3D problem, we report the run time of the proposed method compared with that of Kratos, a parallel, highly optimized finite element code. The results show that in this example, to obtain the same level of error, much less computational effort is needed in the proposed method. Practical limitations might be encountered, however, for large problems because of dense matrix operations involved. Copyright © 2015 John Wiley & Sons, Ltd.

A degenerated shell element with composite implicit time integration scheme is developed in the present paper to solve the geometric nonlinear large deformation and dynamics problems of shell structures. The degenerated shell element is established based on the eight-node solid element, where the nodal forces, mass matrices, and stiffness matrices are firstly obtained upon virtual velocity principle and then translated to the shell element. The strain field is modified based on the mixed interpolation of tensorial components method to eliminate the shear locking, and the constitutive relation is modified to satisfy the shell assumptions. A simple and practical computational method for nonlinear dynamic response is developed by embedding the composite implicit time integration scheme into the degenerated shell element, where the composite scheme combines the trapezoidal rule with the three-point backward Euler method. The developed approach can not only keep the momentum and energy conservation and decay the high frequency modes but also lead to a symmetrical stiffness matrix. Numerical results show that the developed degenerated shell element with the composite implicit time integration scheme is capable of solving the geometric nonlinear large deformation and dynamics problems of the shell structures with momentum and energy conservation and/or decay. Copyright © 2015 John Wiley & Sons, Ltd.

A multiscale numerical technique, termed the seamless-domain method (SDM), is applied to linear elastic problems. The SDM consists of two steps. The first step is a microscopic analysis of the local simulated domain to construct interpolation functions for discretizing governing equations. This allows an SDM solution to represent a structure consisting of heterogeneous microstructure(s) without homogenization. The second step is a macroscopic analysis of a seamless global (entire) domain that has only coarse-grained points and does not need a mesh or grid. The special functions obtained in the first step are used in interpolating the dependent-variable distribution in the global domain. Additionally, the SDM can enhance analytical precision and resolution when analyzing both homogeneous and heterogeneous fields. Our previous manuscript gave numerical examples of the application of the method to scalar temperature fields. To investigate the feasibility of the analysis of vector fields, the SDM technique is applied in linear elastic analysis of heterogeneous materials in the present study. The SDM's global models with only a few hundred points gave shear locking-free and hourglass-free solutions at the same level of accuracy as solutions obtained from conventional finite element analysis using hundreds of thousands of node points or more. Copyright © 2015 John Wiley & Sons, Ltd.

We propose a coupled boundary element method (BEM) and a finite element method (FEM) for modelling localized damage growth in structures. BEM offers the flexibility of modelling large domains efficiently, while the non-linear damage growth is accurately accounted by a local FEM mesh. An integral-type nonlocal continuum damage mechanics with adapting FEM mesh is used to model multiple damage zones and follow their propagation in the structure. Strong form coupling, BEM hosted, is achieved using Lagrange multipliers. Because the non-linearity is isolated in the FEM part of the system of equations, the system size is reduced using Schur complement approach, then the solution is obtained by a monolithic Newton method that is used to solve both domains simultaneously. The coupled BEM/FEM approach is verified by a set of convergence studies, where the reference solution is obtained by a fine FEM. In addition, the method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature. Copyright © 2015 John Wiley & Sons, Ltd.

Fluid–structure interactions (FSI) play a crucial role in many engineering fields. However, the computational cost associated with high-fidelity aeroelastic models currently precludes their direct use in industry, especially for strong interactions. The strongly coupled segregated problem—that results from domain partitioning—can be interpreted as an optimization problem of a fluid–structure interface residual. Multi-fidelity optimization techniques can therefore directly be applied to this problem in order to obtain the solution efficiently. In previous work, it is already shown that aggressive space mapping (ASM) can be used in this context. In this contribution, we extend the research towards the use of space mapping for FSI simulations. We investigate the performance of two other approaches, generalized space mapping and output space mapping, by application to both compressible and incompressible 2D problems. Moreover, an analysis of the influence of the applied low-fidelity model on the achievable speedup is presented. The results indicate that output space mapping is a viable alternative to ASM when applied in the context of solver coupling for partitioned FSI, showing similar performance as ASM and resulting in reductions in computational cost up to 50% with respect to the reference quasi-Newton method. Copyright © 2015 John Wiley & Sons, Ltd.

Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns. Copyright © 2015 John Wiley & Sons, Ltd.

An approach is proposed for the rapid prediction of nano-particle transport and deposition in the human airway, which requires the solution of both the Navier–Stokes and advection–diffusion equations and for which computational efficiency is a challenge. The proposed method builds low-order models that are representative of the fully coupled equations by means of the Galerkin projection and proper orthogonal decomposition technique. The obtained reduced-order models (ROMs) are a set of ordinary differential equations for the temporal coefficients of the basis functions. The numerical results indicate that the ROMs are highly efficient for the computation (the speedup factor is approximately 3 × 10^{3}) and have reasonable accuracy compared with the full model (relative error of ≈7 × 10^{−3}). Using ROMs, the deposition of particles is studied for 1≤*d*_{n}≤100 nm, where *d*_{n} is the diameter of a nano-particle. The effectiveness of this approach is promising for applications of health risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.

A principal issue in any co-rotational approach for large displacement analysis of plates and shells is associated with the specific choice of the local reference system in relation to the current deformed element configuration. Previous approaches utilised local co-rotational systems, which are invariant to nodal ordering, a characteristic that is deemed desirable on several fronts; however, the associated definitions of the local reference system suffered from a range of shortcomings, including undue complexity, dependence on the local element formulation and possibly an asymmetric tangent stiffness matrix. In this paper, new definitions of the local co-rotational system are proposed for quadrilateral and triangular shell elements, which achieve the invariance characteristic to the nodal ordering in a relatively simple manner and address the aforementioned shortcomings. The proposed definitions utilise only the nodal coordinates in the deformed configuration, where two alternative definitions, namely, bisector and zero-macrospin definitions, are presented for each of quadrilateral and triangular finite elements. In each case, the co-rotational transformations linking the local and global element entities are presented, highlighting the simplicity of the proposed approach. Several numerical examples are finally presented to demonstrate the effectiveness and relative accuracy of the alternative definitions proposed for the local co-rotational system. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a new approach for the numerical solution of coupled electromechanical problems is presented. The structure of the considered problem consists of the low-frequency integral formulation of the Maxwell equations coupled with Newton–Euler rigid-body dynamic equations. Two different integration schemes based on the predictor–corrector approach are presented and discussed. In the first method, the electrical equation is integrated with an implicit single-step time marching algorithm, while the mechanical dynamics is studied by a predictor–corrector scheme. The predictor uses the forward Euler method, while the corrector is based on the trapezoidal rule. The second method is based on the use of two interleaved predictor–corrector schemes: one for the electrical equations and the other for the mechanical ones.

Both the presented methods have been validated by comparison with experimental data (when available) and with results obtained by other numerical formulations; in problems characterized by low speeds, both schemes produce accurate results, with similar computation times. When high speeds are involved, the first scheme needs shorter time steps (i.e., longer computation times) in order to achieve the same accuracy of the second one. A brief discussion on extending the algorithm for simulating deformable bodies is also presented. An example of application to a two-degree-of-freedom levitating device based on permanent magnets is finally reported. Copyright © 2015 John Wiley & Sons, Ltd.

The main idea is a dual mathematical formulation and computational implementation of the iterative stochastic perturbation-based finite element method for both linear and nonlinear problems in solid mechanics. A general-order Taylor expansion with random coefficients serves here for the iterative determination of the basic probabilistic characteristics, where linearization procedure widely applicable in stochastic perturbation technique is replaced with the iterative one. The expected values and, in turn, the variances are derived first, and then, they are substituted into the equations for higher central probabilistic moments and additional probabilistic characteristics. The additional formulas for up to the fourth-order probabilistic characteristics are derived thanks to the 10th-order Taylor expansion. Computational implementation of this idea in the stochastic finite element method is provided by using the direct differentiation method and, independently, the response function method with polynomial basis. Numerical experiments include the simple tension of the elastic bar, nonlinear elasto-plastic analysis of the aluminum 2D truss, and solution to the homogenization problem of periodic fiber-reinforced composite with random elastic properties. The expected values, coefficients of variation, skewness, and kurtosis of the structural response determined via this iterative scheme are contrasted with these estimated by the Monte Carlo simulation as well as with the results of the semi-analytical probabilistic technique following the response function method itself. Although the entire methodology is illustrated here by using the Gaussian variables where all odd-order terms simply vanish, it can be extended towards non-Gaussian processes as well and completed with all the perturbation orders. Copyright © 2015 John Wiley & Sons, Ltd.

This article introduces a new algorithm for evaluating enrichment functions in the higher-order hierarchical interface-enriched finite element method (HIFEM), which enables the fully mesh-independent simulation of multiphase problems with intricate morphologies. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along materials interfaces that are in close proximity, in contact, and even intersecting with one another using nonconforming finite element meshes for discretizing the problem. We study different approaches for creating higher-order HIFEM enrichments corresponding to six-node triangular elements and analyze the advantages and shortcomings of each approach. The preferred method, which yields the lowest computational cost and highest accuracy, relies on a special mapping between the local and global coordinate systems for evaluating enrichment functions. A comprehensive convergence study is presented to show that this method yields similar convergence rate and precision as those of the standard FEM with conforming meshes. Finally, we demonstrate the application of the higher-order HIFEM for simulating the thermal and deformation responses of several materials systems and engineering problems with complex geometries. Copyright © 2015 John Wiley & Sons, Ltd.

We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the in case of the conventional polygonal FEM, while it scales as in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Copyright © 2015 John Wiley & Sons, Ltd.

A method of numerical plate testing (NPT) for composite plates with in-plane periodic heterogeneity is proposed. In the two-scale boundary value problem, a thick plate model is employed at macroscale, while three-dimensional solids are assumed at microscale. The NPT, which is nothing more or less than the homogenization analysis, is in fact a series of microscopic analyses on a unit cell that evaluates the macroscopic plate stiffnesses. The specific functional forms of microscopic displacements are originally presented so that the relationship between the macroscopic resultant stresses/moments and strains/curvatures to be consistent with the microscopic equilibrated state. In order to perform NPT by using general-purpose FEM programs, we introduce control nodes to facilitate the multiple-point constraints for in-plane periodicity. Numerical examples are presented to verify that the proposed method of NPT reproduces the plate stiffnesses in classical plate and laminate theories. We also perform a series of homogenization, macroscopic, and localization analyses for an in-plane heterogeneous composite plate to demonstrate the performance of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Thermodynamic irreversibility can be imposed on empirical material behaviour by using an appropriate algorithm which takes the path-dependence of the degradation process into account. This new algorithm, Algorithmically Imposed Mechanics (AIM), for algorithmically irreversible mechanics, is described, and the convergence and unicity of the solutions obtained are proven. AIM is applicable to a range of mechanical behaviour and is demonstrated to work in conjunction with non-local damage with rotating cracks as well as a mixed plastic and damage behaviour. Copyright © 2015 John Wiley & Sons, Ltd.

This study develops a novel multiscale analysis method to predict thermo-mechanical performance of periodic porous materials with interior surface radiation. In these materials, thermal radiation effect at microscale has an important impact on the macroscopic temperature and stress field, which is our particular interest in this paper. Firstly, the multiscale asymptotic expansions for computing the dynamic thermo-mechanical coupling problem, which considers the mutual interaction between temperature and displacement field, are given successively. Then, the corresponding numerical algorithm based on the finite element-difference method is brought forward in details. Finally, some numerical results are presented to verify the validity and relevancy of the proposed method by comparing it with a direct finite element analysis with detailed numerical models. The comparison shows that the new method is effective and valid for predicting the thermo-mechanical performance and can capture the microstructure behavior of periodic porous materials exactly.s Copyright © 2015 John Wiley & Sons, Ltd.

An original state update algorithm for the numerical integration of rate independent small strain elastoplastic constitutive models, treating in a unified manner a wide class of yield functions depending on all three stress invariants, is proposed. The algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free-energy and dissipation potential. Under the assumption of isotropic material behavior, implying coaxiality of trial stress, increment of plastic strain, and updated stress, the problem is reduced from dimension six to three. Then, exploiting the cylindrical tensor basis associated with Haigh–Westergaard coordinates, the problem is recast in terms of two nested scalar equations. The proposed algorithm (i) exhibits global convergence even for yield functions with difficult features, such as not being defined on the whole stress space, or implying high-curvature points of the yield domain, and (ii) requires no matrix inversion. After the tensor reconstruction of the unknowns, a simple expression for the algorithmic consistent material tangent is derived. The algorithm is validated by comparison with benchmark semi-analytic solutions. Numerical results on single material points and finite element simulations are reported for assessing its accuracy, robustness, and efficiency. A Matlab implementation is provided as supplementary material. Copyright © 2015 John Wiley & Sons, Ltd.

An incremental energy minimization approach for the solution of the constitutive equations of 3D phenomenological models for shape memory alloys (SMA) is presented. A robust algorithm for the solution of the resulting nonsmooth constrained minimization problem is devised, without introducing any regularization in the dissipation or chemical terms. The proposed algorithm is based on a thorough detection of the singularities relevant to the incremental energy formulation, in conjunction with a Newton–Raphson method equipped with a Wolfe line search dealing with regular solutions. The saturation constraint on the transformation strain is treated by means of an active set strategy, thus avoiding any need for a two-stage return-mapping algorithm. A parametrization of the saturation constraint manifold is introduced, thus reducing the problem dimensionality, with improved computational performance. Finally, an efficient algorithm for the computation of the dissipation function in terms of Haigh–Westergaard invariants is presented, allowing for a quite general choice of deviatoric transformation functions. Numerical results confirm the robustness and consistency of the proposed state update algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

In digital image correlation (DIC), the unknown displacement field is typically identified by minimizing the linearized form of the brightness conservation equation, while the minimization scheme also involves a linearization, yielding a two-step linearization with four implicit assumptions. These assumptions become apparent by minimizing the non-linear brightness conservation equation in a consistent mathematical setting, yielding a one-step linearization allowing a thorough study of the DIC tangent operator. Through this analysis, eight different image gradient operators are defined, and the impact of these alternative image gradients on the accuracy, efficiency, and initial guess robustness is discussed on the basis of a number of academic examples and representative test cases. The main conclusion is that for most cases, the image gradient most common in literature is recommended, except for cases with: (1) large rotations; (2) initial guess instabilities; and (3) costly iterations due to other reasons (e.g., integrated DIC), where a large deformation corrected mixed gradient is recommended instead. Copyright © 2015 John Wiley & Sons, Ltd.

A critical component of a reduced-order model is the projection that maps the original high-fidelity system on to the reduced-order basis. In this manuscript, we develop a projection for linear systems that is optimal in an operator-independent norm. We derive an expression for this projection as a Galerkin projection plus another component that is interpreted as the effect of the scales that live outside the reduced-order basis. We note that the exact form of this projection does not lead to a viable computational method because it involves the inverse of the original high-fidelity operator. We approximate this inverse by an inexpensive preconditioner and create a practical method whose costs are of the same order as the Galerkin method. We test the performance of this method on heat conduction and advection–diffusion problems while using the incomplete LU preconditioner as an approximate to the inverse of the original operator, and conclude that it provides more accurate results than the Galerkin projection. Copyright © 2015 John Wiley & Sons, Ltd.

We propose a full Eulerian framework for solving fluid-structure interaction (FSI) problems based on a unified formulation in which the FSIs are modelled by introducing an extra stress in the momentum equation. The obtained three-field velocity, pressure and stress system is solved using a stabilized finite element method. The key feature of this unified formulation is the ability to describe different kind of interactions between the fluid and the structure, which can be either elastic or a perfect rigid body, without the need of treating this last case via penalization. The level-set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid-solid interface. Copyright © 2015 John Wiley & Sons, Ltd.

The previously developed bridging cell method for modeling coupled continuum/atomistic systems at finite temperature is used to model fatigue crack growth in single crystal nickel under two crystal orientations at different temperatures. The method is expanded to implement a temperature-dependent embedded atom method potential for finite temperature simulations avoiding time-scale restrictions associated with small timesteps. Results for the fatigue simulation were compared with respect to deformation behavior, stress distribution, and crack length. Results showed very different crack growth mechanisms between the two crystal orientations as well as reduced resistance to crack growth with increased temperature. Copyright © 2015 John Wiley & Sons, Ltd.

Poro-elastic materials are commonly used for passive control of noise and vibration and are key to reducing noise emissions in many engineering applications, including the aerospace, automotive and energy industries. More efficient computational models are required to further optimise the use of such materials. In this paper, we present a discontinuous Galerkin method (DGM) with plane waves for poro-elastic materials using the Biot theory solved in the frequency domain. This approach offers significant gains in computational efficiency and is simple to implement (costly numerical quadratures of highly oscillatory integrals are not needed). It is shown that the Biot equations can be easily cast as a set of conservation equations suitable for the formulation of the wave-based DGM. A key contribution is a general formulation of boundary conditions as well as coupling conditions between different propagation media. This is particularly important when modelling porous materials as they are generally coupled with other media, such as the surround fluid or an elastic structure. The validation of the method is described first for a simple wave propagating through a porous material, and then for the scattering of an acoustic wave by a porous cylinder. The accuracy, conditioning and computational cost of the method are assessed, and comparison with the standard finite element method is included. It is found that the benefits of the wave-based DGM are fully realised for the Biot equations and that the numerical model is able to accurately capture both the oscillations and the rapid attenuation of the waves in the porous material. Copyright © 2015 John Wiley & Sons, Ltd.

An adaptive low-dimensional model is considered to simulate time-dependent dynamics in nonlinear dissipative systems governed by PDEs. The method combines an inexpensive POD-based Galerkin system with short runs of a standard numerical solver that provides the snapshots necessary to first construct and then update the POD modes. Switching between the numerical solver and the Galerkin system is decided ‘on the fly’ by monitoring (i) a truncation error estimate and (ii) a residual estimate. The latter estimate is used to control the mode truncation instability and highly improves former adaptive strategies that detected this instability by monitoring consistency with a second instrumental Galerkin system based on a larger number of POD modes. The most computationally expensive run of the numerical solver occurs at the outset, when the whole set of POD modes is calculated. This step is improved by using mode libraries, which may either be generic or result from former applications of the method. The outcome is a flexible, robust, computationally inexpensive procedure that adapts itself to the local dynamics by using the faster Galerkin system for the majority of the time and few, on demand, short runs of a numerical solver. The method is illustrated considering the complex Ginzburg–Landau equation in one and two space dimensions. Copyright © 2015 John Wiley & Sons, Ltd.

In this article, the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form subject to given initial and Dirichlet boundary conditions. The main difficulty of the great number of methods in full 3-D problems is the large computational costs. In meshless local radial point interpolation method, it does not require any background integration cells, so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions. The point interpolation method with the help of radial basis functions is proposed to construct shape functions that have Kronecker delta function property. A weak formulation with the Heaviside step function converts the set of governing equations into local integral equations on local subdomains. A two-step time discretization method is employed to evaluate the time derivatives. This suggests Crank-Nicolson technique to be applied on the right hand side of the equation. The convergence analysis and stability of the method are fully discussed. Three illustrative examples are presented, and satisfactory agreements are achieved. It is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones. Copyright © 2015 John Wiley & Sons, Ltd.

A multi-material topology optimization scheme is presented. The formulation includes an arbitrary number of phases with different mechanical properties. To ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions, an obstacle potential function, which introduces infinity penalty for negative densities, is utilized. The problem is formulated for nonlinear deformations, and the objective of the optimization is the end displacement. The boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method. To illustrate the possibilities of the method, it is applied to a simple boundary value problem where optimal designs using multiple phases are considered. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a novel reduced integration eight-node solid-shell finite element formulation with hourglass stabilization is proposed. The enhanced assumed strain method is adopted to eliminate the well-known volumetric and Poisson thickness locking phenomena with only one internal variable required. In order to alleviate the transverse shear and trapezoidal locking and correct rank deficiency simultaneously, the assumed natural strain method is implemented in conjunction with the Taylor expansion of the inverse Jacobian matrix. The projection of the hourglass strain-displacement matrix and reconstruction of its transverse shear components are further employed to avoid excessive hourglass stiffness. The proposed solid-shell element formulation successfully passes both the membrane and bending patch tests. Several typical examples are presented to demonstrate the excellent performance and extensive applicability of the proposed element. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letnikov approximation of the fractional derivative.

Moreover, Timoshenko beam response is generally evaluated by solving a couple of differential equations. In this paper, expressing the equation of the elastic curve just through a single relation, a more general procedure, which allows the determination of the beam response for any load condition and type of constraints, is developed. Copyright © 2015 John Wiley & Sons, Ltd.

A methodology aimed at addressing computational complexity of analyzing delamination in large structural components made of laminated composites is proposed. The classical ply-by-ply discretization of individual layers may increase the size of the problem by an order of magnitude in comparison with the laminated shell or plate element meshes. The paper features delamination indicators that pinpoint the onset and propagation of delamination fronts with striking accuracy. Once the location of delamination has been identified, the discrete solution space of the classical laminated plate/shell element is hierarchically enriched by a combination of weak and strong discontinuities to adaptively track the evolution of delamination fronts. The so-called adaptive *s*-method proposed herein is equivalent in terms of approximation space to the extended finite element method but offers sparser matrices and added flexibility in transitioning from weak to strong discontinuities. Numerical examples suggest that despite an overhead that comes with adaptivity, the adaptive *s*-method is computationally advantageous over the classical ply-by-ply discretization, especially as the problem size increases. Copyright © 2015 John Wiley & Sons, Ltd.

A return mapping algorithm in principal stress space for unified strength theory (UST) model is presented in this paper. In contrast to Mohr–Coulomb and Tresca models, UST model contains two planes and three corners in the sextant of principal stress space, and the apex is formed by the intersection of 12 corners rather than the six corners of Mohr–Coulomb in the whole principal stress space. In order to utilize UST model, the existing return mapping algorithm in principal stress space is modified. The return mapping schemes for one plane, middle corner, and apex of UST model are derived, and corresponding consistent constitutive matrices in principal stress space are constructed. Because of the flexibility of UST, the present model is not only suitable for analysis based on the traditional yield functions, such as Mohr–Coulomb, Tresca, and Mises, but might also be used for analysis based on a series of new failure criteria. The accuracy of the present model is assessed by the iso-error maps. Three numerical examples are also given to demonstrate the capability of the present algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

Termed as random media, rocks, composites, alloys and many other heterogeneous materials consist of multiple material phases that are randomly distributed through the medium. This paper presents a robust and efficient algorithm for reconstructing random media, which can then be fed into stochastic finite element solvers for statistical response analysis. The new method is based on nonlinear transformation of Gaussian random fields, and the reconstructed media can meet the discrete-valued marginal probability distribution function and the two-point correlation function of the reference medium. The new method, which avoids iterative root-finding computation, is highly efficient and particularly suitable for reconstructing large-size random media or a large number of samples. Also, benefiting from the high efficiency of the proposed reconstruction scheme, a Karhunen–Loève (KL) representation of the target random medium can be efficiently estimated by projecting the reconstructed samples onto the KL basis. The resulting uncorrelated KL coefficients can be further expressed as functions of independent Gaussian random variables to obtain an approximate Gaussian representation, which is often required in stochastic finite element analysis. Copyright © 2015 John Wiley & Sons, Ltd.

The current work presents an improved immersed boundary method based on the ideas proposed by Vanella and Balaras (M. Vanella, E. Balaras, A moving-least-squares reconstruction for embedded-boundary formulations, J. Comput. Phys. 228 (2009) 6617–6628). In the method, an improved moving-least-squares approximation is employed to build the transfer functions between the Lagrangian points and discrete Eulerian grid points. The main advantage of the improved method is that there is no need to obtain the inverse matrix, which effectively eliminates numerical instabilities caused by matrix inversion and reduces the computational cost significantly. Several different flow problems (Taylor-Green decaying vortices, flows past a stationary circular cylinder and a sphere, and the sedimentation of a free-falling sphere in viscous fluid) are simulated to validate the accuracy and efficiency of the method proposed in the present paper. The simulation results show good agreement with previous numerical and experimental results, indicating that the improved immersed boundary method is efficient and reliable in dealing with the fluid–solid interaction problems. Copyright © 2015 John Wiley & Sons, Ltd.

We consider an optimal model reduction problem for large-scale dynamical systems. The problem is formulated as a minimization problem over Grassmann manifold with two variables. This formulation allows us to develop a two-sided Grassmann manifold algorithm, which is numerically efficient and suitable for the reduction of large-scale systems. The resulting reduced system preserves the stability of the original system. Numerical examples are presented to show that the proposed algorithm is computationally efficient and robust with respect to the selection of initial projection matrices. Copyright © 2015 John Wiley & Sons, Ltd.

A description is given of the development and use of the Reproducing Kernel Particle Finite Strip Method for the buckling and flexural vibration analysis of plates with intermediate supports and step thickness changes. The generalized 1-D shape functions of the Reproducing Kernel Particle Method replace the spline functions in the conventional spline finite strip method in the longitudinal direction. The structure of the generalized Reproducing Kernel Particle Method makes it a suitable tool for dealing with derivative-type essential boundary conditions, and its introduction in the finite strip method is beneficial for solving buckling and vibration problems for thin plates in which a number of the essential boundary conditions can include the first derivatives of the displacement function. Moreover, the modified corrected collocation method is further developed for the buckling and free vibration analysis of plates with abrupt thickness changes. This provides a versatile and powerful analysis capability which facilitates the analysis of problems including plate structures with abrupt thickness changes of its component plates. The application of the proposed technique for the treatment of discontinuities and the enforcement of the internal support conditions are illustrated with a series of numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

A robust approach to nondestructive test (NDT) design for material characterization and damage identification in solids and structures is presented and numerically evaluated. The generally applicable approach combines maximization of test sensitivity with minimization of test information redundancy, while simultaneously minimizing the effects of uncertain system parameters to determine optimal NDT parameters for robust nondestructive evaluation. In addition, to maintain reasonable computational expense while also allowing for general applicability, a stochastic collocation technique is presented for the quantification of uncertainty in the robust design metrics. The robust NDT design approach was tested through simulated case studies based on the characterization of localized variations in Young's modulus distributions in aluminum structural components utilizing steady-state dynamic surface excitation and localized measurements of displacement and compared with a purely deterministic NDT design approach. The robust design approach is shown to produce substantially different NDT designs than the analogous deterministic strategy. More importantly, the robust NDT designs are shown to provide significant improvements in the ability to accurately nondestructively evaluate structural properties for the cases considered, when there is significant uncertainty in system parameters and/or aspects of the NDT implementation. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, we show that the reduced basis method accelerates a partial differential equation constrained optimization problem, where a nonlinear discretized system with a large number of degrees of freedom must be repeatedly solved during optimization. Such an optimization problem arises, for example, from batch chromatography. To reduce the computational burden of repeatedly solving the large-scale system under parameter variations, a parametric reduced-order model with a small number of equations is derived by using the reduced basis method. As a result, the small reduced-order model, rather than the full system, is solved at each step of the optimization process. An adaptive technique for selecting the snapshots is proposed, so that the complexity and runtime for generating the reduced basis are largely reduced. An output-oriented error bound is derived in the vector space whereby the construction of the reduced model is managed automatically. An early-stop criterion is proposed to circumvent the stagnation of the error and to make the construction of the reduced model more efficient. Numerical examples show that the adaptive technique is very efficient in reducing the offline time. The optimization based on the reduced model is successful in terms of the accuracy and the runtime for acquiring the optimal solution. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, an enriched finite element technique is presented to simulate the mechanism of interaction between the hydraulic fracturing and frictional natural fault in impermeable media. The technique allows modeling the discontinuities independent of the finite element mesh by introducing additional DOFs. The coupled equilibrium and flow continuity equations are solved using a staggered Newton solution strategy, and an algorithm is proposed on the basis of fixed-point iteration concept to impose the flow condition at the hydro-fracture mouth. The cohesive crack model is employed to introduce the nonlinear fracturing process occurring ahead of the hydro-fracture tip. Frictional contact is modeled along the natural fault using the penalty method within the framework of plasticity theory of friction. Moreover, an experimental investigation is carried out to perform the hydraulic fracturing experimental test in fractured media under plane strain condition. The results of several numerical and experimental simulations are presented to verify the accuracy and robustness of the proposed computational algorithm as well as to investigate the mechanisms of interaction between the hydraulically driven fracture and frictional natural fault. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a novel numerical framework based on the generalized finite element method with global–local enrichments (GFEM^{gl}) for two-scale simulations of propagating fractures in three dimensions. A non-linear cohesive law is adopted to capture objectively the dissipated energy during the process of material degradation without the need of adaptive remeshing at the macro scale or artificial regularization parameters. The cohesive crack is capable of propagating through the interior of finite elements in virtue of the partition of unity concept provided by the generalized/extended finite element method, and thus eliminating the need of interfacial surface elements to represent the geometry of discontinuities and the requirement of finite element meshes fitting the cohesive crack surface. The proposed method employs fine-scale solutions of non-linear local boundary-value problems extracted from the original global problem in order to not only construct scale-bridging enrichment functions but also to identify damaged states in the global problem, thus enabling accurate global solutions on coarse meshes. This is in contrast with the available GFEM^{gl} in which the local solution field contributes only to the kinematic description of global solutions. The robustness, efficiency, and accuracy of this approach are demonstrated by results obtained from representative numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

This work addresses computational modeling challenges associated with structures subjected to sharp, local heating, where complex temperature gradients in the materials cause three-dimensional, localized, intense stress and strain variation. Because of the nature of the applied loadings, multiphysics analysis is necessary to accurately predict thermal and mechanical responses. Moreover, bridging spatial scales between localized heating and global responses of the structure is nontrivial. A large global structural model may be necessary to represent detailed geometry alone, and to capture local effects, the traditional approach of pre-designing a mesh requires careful manual effort. These issues often lead to cumbersome and expensive global models for this class of problems. To address them, the authors introduce a generalized FEM (GFEM) approach for analyzing three-dimensional solid, coupled physics problems exhibiting localized heating and corresponding thermomechanical effects. The capabilities of traditional *hp*-adaptive FEM or GFEM as well as the GFEM with global–local enrichment functions are extended to one-way coupled thermo-structural problems, providing meshing flexibility at local and global scales while remaining competitive with traditional approaches. The methods are demonstrated on several example problems with localized thermal and mechanical solution features, and accuracy and (parallel) computational efficiency relative to traditional direct modeling approaches are discussed. Copyright © 2015 John Wiley & Sons, Ltd.

The morphology of many natural and man-made materials at different length scales can be simulated using particle-packing methods. This paper presents two novel 3D geometrical collective deposition algorithms for packed assemblies with prescribed distribution of radii: the ‘planar deposition’ and the ‘3D-clew’ method. The ‘planar deposition’ method mimics an orderly granular flow through a funnel by stacking up spirally ordinated planar assemblies of spheres capable of achieving the theoretical maximum for monodisperse aggregates. The ‘3D-clew’ method, instead, mimics the winding of a clew of yarn, thus yielding densely packed 3D polydispersed assemblies in terms of void ratio of the aggregate. The morphologies of such geometrically generated assemblies, achieved at several orders of magnitude reduced computational cost, are comparable with those consolidated uni-directionally by means of discrete element method. In addition, significantly faster simulations of mechanical consolidation of granular media have been performed when relying upon the proposed geometrically generated assemblies as starting configurations. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks. In this method, the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters. The discrete values of the effective potential are computed by finite element method through random sampling in the parameter space, and neural networks are used to approximate the surface response and to derive the macroscopic stress and tangent tensor components. We show through several numerical convergence analyses that smooth functions can be efficiently evaluated in parameter spaces with dimension up to 10, allowing to consider three-dimensional representative volume elements and an explicit dependence of the effective behavior on microstructural parameters like volume fraction. We present several applications of this technique to the homogenization of nonlinear elastic composites, involving a two-scale example of heterogeneous structure with graded nonlinear properties. Copyright © 2015 John Wiley & Sons, Ltd.

Since the inception of discrete element method (DEM) over 30 years ago, significant algorithmic developments have been made to enhance the performance of DEM while emphasizing simulation fidelity. Nevertheless, DEM is still a computationally expensive numerical method for simulation of granular materials. In this study, a new impulse-based DEM (iDEM) approach is introduced that uses collision impulse instead of contact force and directly handles velocity while bypassing integration of acceleration. Contact force required for engineering applications is retrieved with reasonable fidelity via an original proposed formulation. The method is robust, numerically stable and results in significant speed up of almost two orders of magnitude over conventional DEM. The proposed iDEM allows for the simulation of large number of particles within reasonable run times on readily accessible computer hardware. Copyright © 2015 John Wiley & Sons, Ltd.

A two-scale parameter identification approach is investigated. The microscopic material parameters of a two-scale model are identified by comparing macroscopic simulation data with macroscopic full-field measurements of the micro-structured specimen. Gradient-based solution strategies are employed for the optimization problem of the two-scale parameter identification. In particular, two approaches for the gradient calculation are investigated: the finite difference method is compared with a newly introduced semi-analytical scheme. The focus lies on the identification of microscopic elastoplastic material parameters. The presented identification example with artificial data confirms a reduced computational effort and advantageous convergence for the semi-analytical approach within the two-scale parameter identification. A drawback is the increase in memory requirement. Copyright © 2015 John Wiley & Sons, Ltd.

A framework to solve shape optimization problems for quasi-static processes is developed and implemented numerically within the context of isogeometric analysis (IGA). Recent contributions in shape optimization within IGA have been limited to static or steady-state loading conditions. In the present contribution, the formulation of shape optimization is extended to include time-dependent loads and responses. A general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems. An adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of IGA. The methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi-axial tension and pure shear. Under quasi-static loading conditions, the method is validated using a passive control approach with an a priori known solution. Several applications of time-dependent mechanical problems are shown to illustrate the capabilities of this approach. In particular, a problem is considered where an external load is allowed to move along the surface of a structure. The shape of the structure is modified in order to control the time-dependent displacement of the point where the load is applied according to a pre-specified target. Copyright © 2015 John Wiley & Sons, Ltd.

Domain decomposition methods often exhibit very poor performance when applied to engineering problems with large heterogeneities. In particular, for heterogeneities along domain interfaces, the iterative techniques to solve the interface problem are lacking an efficient preconditioner. Recently, a robust approach, named finite element tearing and interconnection (FETI)–generalized eigenvalues in the overlaps (Geneo), was proposed where troublesome modes are precomputed and deflated from the interface problem. The cost of the FETI–Geneo is, however, high. We propose in this paper techniques that share similar ideas with FETI–Geneo but where no preprocessing is needed and that can be easily and efficiently implemented as an alternative to standard domain decomposition methods. In the block iterative approaches presented in this paper, the search space at every iteration on the interface problem contains as many directions as there are domains in the decomposition. Those search directions originate either from the domain-wise preconditioner (in the simultaneous FETI method) or from the block structure of the right-hand side of the interface problem (block FETI). We show on two-dimensional structural examples that both methods are robust and provide good convergence in the presence of high heterogeneities, even when the interface is jagged or when the domains have a bad aspect ratio. The simultaneous FETI was also efficiently implemented in an optimized parallel code and exhibited excellent performance compared with the regular FETI method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper proposes a fuzzy interval perturbation method (FIPM) and a modified fuzzy interval perturbation method (MFIPM) for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions. Interval variables are used to quantify the non-probabilistic uncertainty with limited information, whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions. The level-cut method is introduced to decompose the fuzzy parameters into interval variables. FIPM approximates the interval matrix inverse by the first-order Neumann series, while MFIPM improves the accuracy by considering higher-order terms of the Neumann series. The membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem. Three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters, pure interval parameters, and pure fuzzy parameters, respectively. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a high-order homogenization model for wave propagation in viscoelastic composite structures. Asymptotic expansions with multiple spatial scales are employed to formulate the homogenization model. The proposed multiscale model operates in the Laplace domain allowing the representation of linear viscoelastic constitutive relationship using a proportionality law. The high-order terms in the asymptotic expansion of response fields are included to reproduce micro-heterogeneity-induced wave dispersion and formation of bandgaps. The first and second-order influence functions and the macroscopic deformation are evaluated using the finite element method with complex coefficients in the Laplace domain. The performance of the proposed model is assessed by investigating wave propagation characteristics in layered and particulate composites and verified against direct numerical simulations and analytical solutions. The analysis of dissipated energy revealed that material dispersion may contribute significantly to wave attenuation in dissipative composite materials. The wave dispersion characteristics are shown to be sensitive to microstructure morphology. Copyright © 2015 John Wiley & Sons, Ltd.

A novel approach is presented based upon the Linear Matching Method framework in order to directly calculate the ratchet limit of structures subjected to *arbitrary* thermo-mechanical load histories. Traditionally, ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components, respectively, in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs. The method proposed in this paper, for the first time, accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads, as opposed to an additional primary load only. The method is a strain-based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle. The ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared with the traditional Bree solution. The method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries. Two example problems have been utilised in order to verify the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

The extended finite element method is extended to allow computation of the limit load of cracked structures. In the paper, it is demonstrated that the linear elastic tip enrichment basis with and without radial term may be used in the framework of limit analysis, but the six-function enrichment basis based on the well-known Hutchinson–Rice–Rosengren asymptotic fields appears to be the best. The discrete kinematic formulation is cast in the form of a second-order cone problem, which can be solved using highly efficient interior-point solvers. Finally, the proposed numerical procedure is applied to various benchmark problems, showing that the present results are in good agreement with those in the literature. Copyright © 2015 John Wiley & Sons, Ltd.

A novel global digital image correlation method was developed using adaptive refinement of isogeometric shape functions. Non-uniform rational B-spline shape functions are used because of their flexibility and versatility, which enable them to capture a wide range of kinematics. The goal of this work was to explore the full potential of isogeometric shape functions for digital image correlation (DIC). This is reached by combining a global DIC method with an adaptive refinement algorithm: adaptive isogeometric GDIC. The shape functions are automatically adjusted to be able to describe the kinematics of the sought displacement field with an optimized number of degrees of freedom. This results in an accurate method without the need of making problem-specific choices regarding the structure of the shape functions, which makes the method less user input dependent than regular global DIC methods, while keeping the number of degrees of freedom limited to realize optimum regularization of the ill-posed DIC problem. The method's accuracy is demonstrated by a virtual experiment with a predefined, highly localized displacement field. Real experiments with a complex sample geometry demonstrate the effectiveness in practice. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, a 2D finite element (FE) formulation for a multi-layer beam with arbitrary number of layers with interconnection that allows for mixed-mode delamination is presented. The layers are modelled as linear beams, while interface elements with embedded cohesive-zone model are used for the interconnection. Because the interface elements are sandwiched between beam FEs and attached to their nodes, the only basic unknown functions of the system are two components of the displacement vector and a cross-sectional rotation per layer. Damage in the interface is modelled via a bi-linear constitutive law for a single delamination mode and a mixed-mode damage evolution law. Because in a numerical integration procedure, the damage occurs only in discrete integration points (i.e. not continuously), the solution procedure experiences sharp snap backs in the force-displacements diagram. A modified arc-length method is used to solve this problem. The present model is verified against commonly used models, which use 2D plane-strain FEs for the bulk material. Various numerical examples show that the multi-layer beam model presented gives accurate results using significantly less degrees of freedom in comparison with standard models from the literature. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a new optimization technique applicable to optimization of composite structures subjected to multiple objectives. The composite structures may be composed of an arbitrary number of laminates. The technique is especially suited for the case where the layers of the laminates may assume a discrete number of orientations. However, given the efficiency of the technique, it is readily extendable to situations where the ply orientations vary quasi-continuously, for instance, by one degree in one degree. The high efficiency is obtained through application of lamination parameters, which, in the case of symmetric laminates, consist of only 10 parameters per laminate. Three traditional structures, a rectangular composite plate, a cantilever composite beam, and a stiffened composite panel, are optimized against buckling when subjected to multiple load cases. Copyright © 2015 John Wiley & Sons, Ltd.

We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state-discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.

In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen–Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.

A new constitutive algorithm for the rate-independent crystal plasticity is presented. It is based on asymptotically exact formulation of the set of constitutive equations and inequalities as a minimum problem for the incremental work expressed by a quadratic function of non-negative crystallographic slips. This approach requires selective symmetrization of the slip-system interaction matrix restricted to active slip-systems, while the latent hardening rule for inactive slip-systems is arbitrary. The active slip-system set and incremental slips are determined by finding a constrained minimum point of the incremental work. The solutions not associated with a local minimum of the incremental work are automatically eliminated in accord with the energy criterion of path stability. The augmented Lagrangian method is applied to convert the constrained minimization problem to a smooth unconstrained one. Effectiveness of the algorithm is demonstrated by the large deformation examples of simple shear of a face-centered cubic (fcc) crystal and rolling texture in a polycrystal. The algorithm is extended to partial kinematic constraints and applied to a uniaxial tension test in a high-symmetry direction, showing the ability of the algorithm to cope with the non-uniqueness problem and to generate experimentally observable solutions with a reduced number of active slip-systems. Copyright © 2015 John Wiley & Sons, Ltd.

A coupling extended multiscale finite element method (CEMsFEM) is developed for the dynamic analysis of heterogeneous saturated porous media. The coupling numerical base functions are constructed by a unified method with an equivalent stiffness matrix. To improve the computational accuracy, an additional coupling term that could reflect the interaction of the deformations among different directions is introduced into the numerical base functions. In addition, a kind of multi-node coarse element is adopted to describe the complex high-order deformation on the boundary of the coarse element for the two-dimensional dynamic problem. The coarse element tests show that the coupling numerical base functions could not only take account of the interaction of the solid skeleton and the pore fluid but also consider the effect of the inertial force in the dynamic problems. On the other hand, based on the static balance condition of the coarse element, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the CEMsFEM. Both one-dimensional and two-dimensional numerical examples of the heterogeneous saturated porous media are carried out, and the results verify the validity and the efficiency of the CEMsFEM by comparing with the conventional finite element method. Copyright © 2015 John Wiley & Sons, Ltd.

A graphics processor units(GPU)-based computational framework is presented to deal with dynamic failure events simulated by means of cohesive zone elements. The work is divided into two parts. In the first part, we deal with pre-processing of the information and verify the effectiveness of dynamic insertion of cohesive elements in large meshes in parallel. To this effect, we employ a novel and simplified topological data structure specialized for meshes with triangles, designed to run efficiently and minimize memory occupancy on the GPU. In the second part, we present a parallel explicit dynamics code that implements an extrinsic cohesive zone formulation where the elements are inserted ‘on-the-fly’, when needed and where needed. The main challenge for implementing a GPU-based computational framework using an extrinsic cohesive zone formulation resides on being able to dynamically adapt the mesh, in a consistent way, by inserting cohesive elements on fractured facets. In order to handle that, we extend the conventional data structure used in the finite element method (based on element incidence) and store, for each element, references to the adjacent elements. This additional information suffices to consistently insert cohesive elements by duplicating nodes when needed. Currently, our data structure is specialized for triangular meshes, but an extension to tetrahedral meshes is feasible. The data structure is effective when used in conjunction with algorithms to traverse nodes and elements. Results from parallel simulations show an increase in performance when adopting strategies such as distributing different jobs among threads for the same element and launching many threads per element. To avoid concurrency on accessing shared entities, we employ graph coloring. In a pre-processing phase, each node of the dual graph (bulk elements of the mesh as graph nodes) is assigned a color different from the colors assigned to adjacent nodes. In that fashion, elements of the same color can be processed in parallel without concurrency. All the procedures needed for the insertion of cohesive elements along fracture facets and for computing nodal properties are performed by threads assigned to triangles, invoking one kernel per color. Computations on existing cohesive elements are also performed based on adjacent bulk elements. Experiments show that GPU speedup increases with the number of nodes and bulk elements. Copyright © 2015 John Wiley & Sons, Ltd.

This work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of Reissner–Mindlin thick plates in shear-bending interaction. The main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields. In particular, it has been demonstrated for 2D plane stress, plane strain or 3D limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates. For this reason, discontinuous interpolations of the transverse velocity and the rotation fields for Reissner–Mindlin plates are proposed. The subsequent discrete minimization problem is formulated as a second-order cone programming problem and is solved using the industrial software package MOSEK. A comprehensive study of the shear-locking phenomenon is also conducted, and it is shown that discontinuous elements avoid such a phenomenon quite naturally whereas continuous elements cannot without any specific treatment. This particular aspect is confirmed through numerical examples on classical benchmark problems and the so-obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates. Copyright © 2015 John Wiley & Sons, Ltd.

Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack-like features with a high degree of variability in the geometry and material properties of the welded structure. Accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. Traditional modeling approaches cannot be efficiently employed. To this end, a method is presented for constructing a surrogate model, based on stochastic reduced-order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking – and thus peak load – plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results. Copyright © 2015 John Wiley & Sons, Ltd.