A multi-material topology optimization scheme is presented. The formulation includes an arbitrary number of phases with different mechanical properties. The 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 non-linear 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. This article is protected by copyright. All rights reserved.

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.

In this article, the meshless local radial point interpolation (MLRPI) method is applied to analyze three space dimensional wave equation of the form *u*_{tt} + *αu*_{t} + *βu* = *u*_{xx} + *u*_{yy} + *u*_{zz} + *f*(*x*, *y*, *z*, *t*), **x**^{T} = (*x*, *y*, *z*) ∈ Ω ⊆ ℝ^{d}, (*d* = 2, 3), *t* > 0 subject to given initial and Dirichlet boundary conditions. The main difficulty of the great number of methods in fully 3-D problems is the large computational costs. In MLRPI 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 which 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 the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones. This article is protected by copyright. All rights reserved.

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. This article is protected by copyright. All rights reserved.

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. This article is protected by copyright. All rights reserved.

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. This article is protected by copyright. All rights reserved.

An adaptive low dimensional model is considered to simulate time dependent dynamics in nonlinear dissipative systems governed by partial differential equations. 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. This article is protected by copyright. All rights reserved.

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. This article is protected by copyright. All rights reserved.

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 to 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. This article is protected by copyright. All rights reserved.

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. This article is protected by copyright. All rights reserved.

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. This article is protected by copyright. All rights reserved.

In this work, we show that the reduced basis method accelerates a PDE 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 getting the optimal solution. This article is protected by copyright. All rights reserved.

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 to the laminated shell or plate element meshes. The manuscript 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. This article is protected by copyright. All rights reserved.

A return mapping algorithm in principal stress space for Unified Strength Theory (UST) model is presented in this paper. In contrast to Mohr-Coulomb, Tresca model, 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 6 corners for Mohr-Coulomb in 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 present model is assessed by the iso-error maps. Three numerical examples are also given to demonstrate the capability of the present algorithm. This article is protected by copyright. All rights reserved.

A description is given of the development and use of the Reproducing Kernel Particle Finite Strip Method (RKP-FSM) [1] 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 (RKPM) replace the spline functions in the conventional spline finite strip method (SFSM) in the longitudinal direction. The structure of the generalized RKPM makes it a suitable tool for dealing with derivative-type essential boundary conditions and its introduction in the finite strip method (FSM) 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 [1, 2] 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. This article is protected by copyright. All rights reserved.

The low-rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low-rank damping property, we propose a Padé Approximate Linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only *n* + *ℓ**m*, which is generally substantially smaller than the dimension 2*n* of the linear eigenvalue problem produced by a direct linearization approach, where *n* is the dimension of the quadratic eigenvalue problem, *ℓ* and *m* are the rank of the damping matrix and the order of a Padé approximant, respectively. Numerical examples show that by exploiting the low-rank damping property, the PAL algorithm runs 33 – 47% faster than the direct linearization approach for solving modest size quadratic eigenvalue problems. This article is protected by copyright. All rights reserved.

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 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.

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.

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.

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.

Excitations of disordered systems such as glasses are of fundamental and practical interest but computationally very expensive to solve. Here, we introduce a technique for modeling these excitations in an infinite disordered medium with a reasonable computational cost. The technique relies on a discrete atomic model to simulate the low-energy behavior of an atomic lattice with molecular impurities. The interaction between different atoms is approximated using a spring-like interaction based on the Lennard-Jones potential, but the method can be easily adapted to other potentials. The technique allows to solve a statistically representative number of samples with low computational expense and uses a Monte Carlo approach to achieve a state corresponding to any given temperature. This technique has already been applied successfully to a problem with interest in condensed matter physics: the solid solution of N_{2} in Ar. 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.

In this paper, a framework for computational homogenization of shell structures is proposed in the context of small-strain elastostatics, with extensions to large displacements and large rotations. At the macroscopic scale, heterogeneous thin structures are modeled using a homogenized shell model, based on a versatile three-dimensional seven-parameter shell formulation, incorporating a through-thickness and pre-integrated constitutive relationship. In the context of small strains, we show that the local solution on the elementary cell can be decomposed into six strains and six-strain gradient modes, associated with corresponding boundary conditions. The heterogeneities can have arbitrary morphology but are assumed to be periodically distributed in the tangential direction of the shell. We then propose an extension of the small-strain framework to geometrical nonlinearities. The procedure is purely sequential and does not involve coupling between scales. The homogenization method is validated and illustrated through examples involving large displacements and buckling of heterogeneous plates and shells. Copyright © 2015 John Wiley & Sons, Ltd.

The ability to model crack-closure behaviour and aggregate interlock in finite element concrete models is extremely important. Both of these phenomena arise from the same contact mechanisms, and the advantages of modelling them in a unified manner are highlighted. An example illustrating the numerical difficulties that arise when abrupt crack closure is modelled is presented, and the benefits of smoothing this behaviour are discussed. We present a new crack-plane model that uses an effective contact surface derived directly from experimental data and which is described by a signed-distance function in relative-displacement space. The introduction of a crack-closure transition function into the formulation improves its accuracy and enhances its robustness. The characteristic behaviour of the new smoothed crack-plane model is illustrated for a series of relative-displacement paths. We describe a method for incorporating the model into continuum elements using a crack-band approach and address a previously overlooked issue associated with scaling the inelastic shear response of a crack band. A consistent algorithmic tangent and associated stress recovery procedure are derived. Finally, a series of examples are presented, demonstrating that the new model is able to represent a range of cracked concrete behaviour with good accuracy and robustness. Copyright © 2015 John Wiley & Sons, Ltd.

The use of the interaction integral to compute stress intensity factors around a crack tip requires selecting an auxiliary field and a material variation field. We formulate a family of these fields accounting for the curvilinear nature of cracks that, in conjunction with a discrete formulation of the interaction integral, yield optimally convergent stress intensity factors. In particular, we formulate three pairs of auxiliary and material variation fields chosen to yield a simple expression of the interaction integral for different classes of problems. The formulation accounts for crack face tractions and body forces. Distinct features of the fields are their ease of construction and implementation. The resulting stress intensity factors are observed converging at a rate that doubles that of the stress field. We provide a sketch of the theoretical justification for the observed convergence rates and discuss issues such as quadratures and domain approximations needed to attain such convergent behavior. Through two representative examples, a circular arc crack and a loaded power function crack, we illustrate the convergence rates of the computed stress intensity factors. The numerical results also show the independence of the method from the size of the domain of integration. Copyright © 2015 John Wiley & Sons, Ltd.

Moment-independent regional sensitivity analysis (RSA) is a very useful guide tool for assessing the effect of a specific range of an individual input on the uncertainty of model output, while large computational burden is involved to perform RSA, which would certainty lead to the limitation of engineering application. Main tasks for performing RSA are to estimate the probability density function (PDF) of model output and the joint PDF of model output and the input variable by some certain smart techniques. Firstly, a method based on the concepts of maximum entropy, fractional moment and sparse grid integration is utilized to estimate the PDF of the model output. Secondly, Nataf transformation is applied to obtain the joint PDF of model output and the input variable. Finally, according to an integral transformation, those regional sensitivity indices can be easily computed by a Monte Carlo procedure without extra function evaluations. Because all the PDFs can be estimated with great efficiency, and only a small amount of function evaluations are involved in the whole process, the proposed method can greatly decrease the computational burden. Several examples with explicit or implicit input–output relations are introduced to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper describes a *modified extended finite element method* (XFEM) approach, which is designed to ease the challenge of an analytical design sensitivity analysis in the framework of structural optimisation. This novel formulation, furthermore labelled *YFEM*, combines the well-known XFEM enhancement functions with a local sub-meshing strategy using standard finite elements. It deviates slightly from the XFEM path only at one significant point but thus allows to use already derived residual vectors as well as stiffness and pseudo load matrices to assemble the desired information on cut elements without tedious and error-prone re-work of already performed derivations and implementations. The strategy is applied to sensitivity analysis of interface problems combining areas with different linear elastic material properties. Copyright © 2015 John Wiley & Sons, Ltd.

We present a monolithic geometric multigrid solver for fluid-structure interaction problems in Arbitrary Lagrangian Eulerian coordinates. The coupled dynamics of an incompressible fluid with nonlinear hyperelastic solids gives rise to very large and ill conditioned systems of algebraic equations. Direct solvers usually are out of question due to memory limitations, standard coupled iterative solvers are seriously affected by the bad condition number of the system matrices. The use of partitioned preconditioners in Krylov subspace iterations is an option, but the convergence will be limited by the outer partitioning. Our proposed solver is based on a Newton linearization of the fully monolithic system of equations, discretized by a Galerkin finite element method. Approximation of the linearized systems is based on a monolithic GMRES iteration, preconditioned by a geometric multigrid solver. The special character of fluid-structure interactions is accounted for by a partitioned scheme within the multigrid smoother only. Here, fluid and solid field are segregated as Dirichlet-Neumann coupling. We demonstrate the efficiency of the multigrid iteration by analyzing 2d and 3d benchmark problems. While 2d problems are well manageable with available direct solvers, challenging 3d problems highly benefit from the resulting multigrid solver. This article is protected by copyright. All rights reserved.

The solution of a steady thermal multiphase problem is assumed to be dependent on a set of parameters describing the geometry of the domain, the internal interfaces and the material properties. These parameters are considered as new independent variables. The problem is therefore stated in a multidimensional setup. The proper generalized decomposition (PGD) provides an approximation scheme especially well suited to preclude dramatically increasing the computational complexity with the number of dimensions. The PGD strategy is reviewed for the standard case dealing only with material parameters. Then, the ideas presented in [Ammar *et al.*, “Parametric solutions involving geometry: A step towards efficient shape optimization.” *Comput. Methods Appl. Mech. Eng.*, 2014; **268**:178–193] to deal with parameters describing the domain geometry are adapted to a more general case including parametrization of the location of internal interfaces. Finally, the formulation is extended to combine the two types of parameters. The proposed strategy is used to solve a problem in applied geophysics studying the temperature field in a cross section of the Earth crust subsurface. The resulting problem is in a 10-dimensional space, but the PGD solution provides a fairly accurate approximation (error ≤1*%*) using less that 150 terms in the PGD expansion. Copyright © 2015 John Wiley & Sons, Ltd.

An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo-hydro-mechanical behavior of porous media undergoing large deformation. We first formulate a finite-deformation thermo-hydro-mechanics field theory for non-isothermal porous media. Projection-based stabilization procedure is derived to eliminate spurious pore pressure and temperature modes due to the lack of the two-fold inf-sup condition of the equal-order finite element. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non-isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this thermo-hydro-mechanical model. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents an examination of moving-boundary temperature control problems. With a moving-boundary problem, a finite-element mesh is generated at each time step to express the position of the boundary. On the other hand, if an overlapped domain, that is, comprising foreground and background meshes, is prepared, the moving boundary problem can be solved without mesh generation at each time step by using the fictitious domain method. In this study, boundary temperature control problems with a moving boundary are formulated using the finite element, the adjoint variable, and the fictitious domain methods, and several numerical experiments are carried out. Copyright © 2015 John Wiley & Sons, Ltd.

We determine linear dependencies and the partition of unity property of T-spline meshes of arbitrary degree using the Bézier extraction operator. Local refinement strategies for standard, semi-standard and non-standard T-splines – also by making use of the Bézier extraction operator – are presented for meshes of even and odd polynomial degrees. A technique is presented to determine the nesting between two T-spline meshes, again exploiting the Bézier extraction operator. Finally, the hierarchical refinement of standard, semi-standard and non-standard T-spline meshes is discussed. This technique utilises the reconstruction operator, which is the inverse of the Bézier extraction operator. Copyright © 2015 John Wiley & Sons, Ltd.

A generalised Voronoi tessellation is proposed to create three-dimensional microstructural finite element model, which can effectively reproduce the grain size distribution and grain aspect ratio obtained from experiments. This new approach consists of two steps. The first step generates the desired lognormal grain size distribution with a given average grain volume and standard deviation. The second step requires grouping meshed elements to create a specific grain aspect ratio, using the Voronoi generators from the first step. A new concept is introduced to describe the transition from the Poisson–Voronoi tessellation to the centroidal Voronoi tessellation. More importantly, instead of using the conventional way where the Voronoi cells are first generated and then meshed into finite elements, this new approach discretises the pre-meshed specimen with the Voronoi generators. This new technique prevents the presence of high density mesh at the vertices of Voronoi cells, and can tessellate irregular geometry much more easily. Examples of microstructures with different size distributions, non-equiaxed grains and complicated specimen geometries further demonstrate that the proposed approach can offer great flexibility to model various specimen geometries while keeping the process simple and efficient. Copyright © 2015 John Wiley & Sons, Ltd.

When applying the combined finite-discrete element method for analysis of dynamic problems, contact is often encountered between the finite elements and discrete elements, and thus an effective contact treatment is essential. In this paper, an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles, which represent rigid discrete elements, and convex quadrilateral mesh facets, which represent finite element boundaries of structural components. Different contact scenarios between particles and mesh facets, or edges, or vertices have been taken into account. For each potential contact pair, the contact search is performed in an hierarchical way starting from mesh facets, possibly going to edges and even further to vertices. The invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications. This hierarchical contact searching scheme is effective, and its implementation is straightforward. Numerical examples demonstrated the accuracy and robustness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

A method for stabilizing the mean-strain hexahedron for applications to anisotropic elasticity was described by Krysl (in IJNME 2014). The technique relied on a sampling of the stabilization energy using the mean-strain quadrature and the full Gaussian integration rule. This combination was shown to guarantee consistency and stability. The stabilization energy was expressed in terms of input parameters of the real material, and the value of the stabilization parameter was fixed in a quasi-optimal manner by linking the stabilization to the bending behavior of the hexahedral element (Krysl, submitted). Here, the formulation is extended to large-strain hyperelasticity (as an example, the formulation allows for inelastic behavior to be modeled). The stabilization energy is expressed through a stored-energy function, and contact with input parameters in the small-strain regime is made. As for small-strain elasticity, the stabilization parameter is determined to optimize bending performance. The accuracy and convergence characteristics of the present formulations for both solid and thin-walled structures (shells) compare favorably with the capabilities of mean-strain and other high-performance hexahedral elements described in the open literature and also with a number of successful shell elements. Copyright © 2015 John Wiley & Sons, Ltd.

We present an embedded boundary method for the interaction between an inviscid compressible flow and a fragmenting structure. The fluid is discretized using a finite volume method combining Lax–Friedrichs fluxes near the opening fractures, where the density and pressure can be very low, with high-order monotonicity-preserving fluxes elsewhere. The fragmenting structure is discretized using a discrete element method based on particles, and fragmentation results from breaking the links between particles. The fluid-solid coupling is achieved by an embedded boundary method using a cut-cell finite volume method that ensures exact conservation of mass, momentum, and energy in the fluid. A time explicit approach is used for the computation of the energy and momentum transfer between the solid and the fluid. The embedded boundary method ensures that the exchange of fluid and solid momentum and energy is balanced. Numerical results are presented for two-dimensional and three-dimensional fragmenting structures interacting with shocked flows. Copyright © 2015 John Wiley & Sons, Ltd.

A methodology is proposed in this paper to construct an adaptive sparse polynomial chaos (PC) expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields. The proposed methodology utilizes the concept of variability response function in order to compute an a priori low-cost estimate of the spatial distribution of the second-order error of the response, as a function of the number of terms used in the truncated Karhunen–Loève (KL) expansion. This way the influence of the response variance to the spectral content (correlation structure) of the random input is taken into account through a spatial variation of the truncated KL terms. The criterion for selecting the number of KL terms at different parts of the structure is the uniformity of the spatial distribution of the second-order error. This way a significantly reduced number of PC coefficients, with respect to classical PC expansion, is required in order to reach a uniformly distributed target second-order error. This results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper proposes a novel Immersed Boundary Method where the embedded domain is exactly described by using its Computer-Aided Design (CAD) boundary representation with Non-Uniform Rational B-Splines (NURBS) or T-splines. The common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation. In contrast, the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain. A novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests. The applicability, performance, and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions. It is also shown that the accuracy of the proposed methodology is independent on the CAD technology used to describe the geometry of the embedded domain. Copyright © 2015 John Wiley & Sons, Ltd.

Structures made of shape memory polymer composite (SMPC), due to their ability to be formed into a desired compact loading shape and then transformed back to their original aperture by means of an applied stimulus, are an ideal solution to deployment problems of large and lightweight space structures. In the literature, there is a wide array of work on constitutive laws and qualitative analyses of SMP materials; dynamic equations and numerical solution methods for SMPC structures have rarely been addressed. In this work, a macroscopic model for the shape fixation and shape recovery processes of SMPC structures and a finite element formulation for relevant numerical solutions are developed. To demonstrate basic concepts, a cantilever SMPC beam is used in the presentation. In the development, a quasi-static beam model that combines geometric nonlinearity in beam deflection with a temperature-dependent constitutive law of SMP material is obtained, which is followed by derivation of the dynamic equations of the SMPC beam. Furthermore, several finite element models are devised for numerical solutions, which include both beam and shell elements. Finally, in numerical simulation, the quasi-static SMPC beam model is used to show the physical behaviors of the SMPC beam in shape fixation and shape recovery. Copyright © 2015 John Wiley & Sons, Ltd.

The computational complexity behind the bi-level optimization problem has led the researchers to adopt Karush–Kuhn–Tucker (KKT) optimality conditions. However, the problem function has more number of complex constraints to be satisfied. Classical optimization algorithms are impotent to handle the function. This paper presents a simplified minimization function, in which both the profit maximization problem and the ISO market clearance problem are considered, but with no KKT optimality conditions. Subsequently, this paper solves the minimization function using a hybrid optimization algorithm. The hybrid optimization algorithm is developed by combining the operations of group search optimizer (GSO) and genetic algorithm (GA). The hybridization enables the dispersion process of GSO to be a new mutated dispersion process for improving the convergence rate. We evaluate the methodology by experimenting on IEEE 14 and IEEE 30 bus systems. The obtained results are compared with the outcomes of bidding strategies that are based on GSO, PSO, and GA. The results demonstrate that the hybrid optimization algorithm solves the minimization function better than PSO, GA, and GSO. Hence, the profit maximization in the proposed methodology is relatively better than that of the conventional algorithms. Copyright © 2015 John Wiley & Sons, Ltd.

Micromechanics modeling, utilizing a cylindrical method of cells (CMOC) model, is employed to obtain the effective mechanical properties of an elastic transversely isotropic, isothermal material system consisting of a hollow carbon nanotube (CNT) embedded in an isotropic polymeric material matrix. It is shown that weak interfacial bonding between the CNT and polymeric matrix, which is characteristic of this type of material system, can be modeled with the CMOC. Numerical solutions of the effective independent material constants are obtained, based upon appropriate values of the properties of the carbon nanotube and epoxy matrix. The numerical results are presented graphically and compared with corresponding classical closed-form solutions. Copyright © 2015 John Wiley & Sons, Ltd.

In this contribution, a mortar-type method for the coupling of non-conforming NURBS (Non-Uniform Rational B-spline) surface patches is proposed. The connection of non-conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor-product structure of NURBS surfaces. Thus, methods to handle non-conforming meshes are essential in NURBS-based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master-slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given. Copyright © 2015 John Wiley & Sons, Ltd.

We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace–Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method. Copyright © 2015 John Wiley & Sons, Ltd.

Inter-phase momentum coupling for particle flows is usually achieved by means of direct numerical simulation (DNS) or point source method (PSM). DNS requires the mesh size of the continuous phase to be much smaller than the size of the smallest particle in the system, whereas PSM requires the mesh size of the continuous phase to be much larger than the particle size. However, for applications where mesh sizes are similar to the size of particles in the system, neither DNS nor PSM is suitable. In order to overcome the dependence of mesh on particle sizes associated with DNS or PSM, a two-layer mesh method (TMM) is proposed. TMM involves the use of a coarse mesh to track the movement of particle clouds and a fine mesh for the continuous phase, with mesh interpolation for information exchange between the coarse and fine mesh Numerical tests of different interpolation methods show that a conservative interpolation scheme of the second order yields the most accurate results. Numerical simulations of a fluidized bed show that there is a good agreement between predictions using TMM with a second-order interpolation scheme and the experimental results, as well as predictions obtained with PSM. Copyright © 2015 John Wiley & Sons, Ltd.

We investigate the issue of sub-kernel spurious interface fragmentation occurring in SPH applied for multiphase flows. It has appeared recently that current SPH formulations for multiphase flows involving an interface between immiscible phases can suffer from non-physical particle mixing through the interface, especially for flows with high density ratios. This is an important issue, in particular for applications where physical phenomena take place at the interface itself, such as phase change or the evolution of two-phase flow patterns. In this paper, various remedies proposed in the literature are discussed. The current assumption that spurious interface fragmentation occurs only when there is no surface tension at the interface is revisited. We show that this is a general problem of current SPH formulations that appears even when surface tension is present. A new proposition for an interface sharpness correction term is put forward. A series of simulations of two-dimensional and three-dimensional bubbles rising in a liquid allow a comprehensive study and demonstrate the dependence of the new correction term on the kernel smoothing length. On the other hand, the overall flow behavior, including the interface shape, is not affected. Copyright © 2015 John Wiley & Sons, Ltd.

With the development of full-field measurement techniques, it has been possible to analyze crack propagation experimentally with an increasing level of robustness. However, the analysis of curved cracks is made difficult and almost unexplored because the possible analysis domain size decreases with crack curvature, leading to an increasing uncertainty level. This paper proposes a digital image correlation technique, augmented by an elastic regularization, combining finite element kinematics on an adapted mesh and a truncated Williams' expansion. Through the analysis of two examples, the proposed technique is shown to be able to address the experimental problems of crack tip detection and stress intensity factors estimation along a curved crack path. Copyright © 2015 John Wiley & Sons, Ltd.

This study proposes smoothed particle hydrodynamics (SPH) in a generalized coordinate system. The present approach allocates particles inhomogeneously in the Cartesian coordinate system and arranges them via mapping in a generalized coordinate system in which the particles are aligned at a uniform spacing. This characteristic enables us to employ fine division only in the direction required, for example, in the through-thickness direction for a thin-plate problem and thus to reduce computation cost. This study provides the formulation of SPH in a generalized coordinate system with a finite-deformation constitutive model and then verifies it by analyzing quasi-static and dynamic problems of solids. High-velocity impact test was also performed with an aluminum target and a steel sphere, and the predicted crater shape agreed well with the experiment. Furthermore, the numerical study demonstrated that the present approach successfully reduced the computation cost with marginal degradation of accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

The Difference Potential Method (DPM) proved to be a very efficient tool for solving boundary value problems (BVPs) in the case of complex geometries. It allows BVPs to be reduced to a boundary equation without the knowledge of Green's functions. The method has been successfully used for solving very different problems related to the solution of partial differential equations. However, it has mostly been considered in regular (Lipschitz) domains. In the current paper, for the first time, the method has been applied to a problem of linear elastic fracture mechanics. This problem requires solving BVPs in domains containing cracks. For the first time, DPM technology has been combined with the finite element method. Singular enrichment functions, such as those used within the extended finite element formulations, are introduced into the system in order to improve the approximation of the crack tip singularity. Near-optimal convergence rates are achieved with the application of these enrichment functions. For the DPM, the reduction of the BVP to a boundary equation is based on generalised surface projections. The projection is fully determined by the clear trace. In the current paper, for the first time, the minimal clear trace for such problems has been numerically realised for a domain with a cut. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we propose a new component mode synthesis method by enhancing the Craig–Bampton (CB) method. To develop the enhanced CB method, the transformation matrix of the CB method is enhanced considering the effect of residual substructural modes and the unknown eigenvalue in the enhanced transformation matrix is approximated by using O'Callahan's approach in Guyan reduction. Using the newly defined transformation matrix, original finite element models can be more accurately approximated by reduced models. For this reason, the accuracy of the reduced models is significantly improved with a low additional computational cost. We here present the formulation details of the enhanced CB method and demonstrate its performance through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.

This work deals with the question of the resolution of nonlinear problems for many different configurations in order to build a ‘virtual chart’ of solutions. The targeted problems are three-dimensional structures driven by Chaboche-type elastic-viscoplastic constitutive laws. In this context, parametric analysis can lead to highly expensive computations when using a direct treatment. As an alternative, we present a technique based on the use of the time-space proper generalized decomposition in the framework of the LATIN method. To speed up the calculations in the parametrized context, we use the fact that at each iteration of the LATIN method, an approximation over the entire time-space domain is available. Then, a global reduced-order basis is generated, reused and eventually enriched, by treating, one-by-one, all the various parameter sets. The novelty of the current paper is to develop a strategy that uses the reduced-order basis for any new set of parameters as an initialization for the iterative procedure. The reduced-order basis, which has been built for a set of parameters, is reused to build a first approximation of the solution for another set of parameters. An error indicator allows adding new functions to the basis only if necessary. The gain of this strategy for studying the influence of material or loading variability reaches the order of 25 in the industrial examples that are presented. Copyright © 2015 John Wiley & Sons, Ltd.

This report presents a numerical study of reduced-order representations for simulating incompressible Navier–Stokes flows over a range of physical parameters. The reduced-order representations combine ideas of approximation for nonlinear terms, of local bases, and of least-squares residual minimization. To construct the local bases, temporal snapshots for different physical configurations are collected automatically until an error indicator is reduced below a user-specified tolerance. An adaptive time-integration scheme is also employed to accelerate the generation of snapshots as well as the simulations with the reduced-order representations. The accuracy and efficiency of the different representations is compared with examples with parameter sweeps. Copyright © 2015 John Wiley & Sons, Ltd.

This paper studies the static fracture problems of an interface crack in linear piezoelectric bimaterial by means of the extended finite element method (X-FEM) with new crack-tip enrichment functions. In the X-FEM, crack modeling is facilitated by adding a discontinuous function and crack-tip asymptotic functions to the classical finite element approximation within the framework of the partition of unity. In this work, the coupled effects of an elastic field and an electric field in piezoelectricity are considered. Corresponding to the two classes of singularities of the aforementioned interface crack problem, namely, *ϵ* class and *κ* class, two classes of crack-tip enrichment functions are newly derived, and the former that exhibits oscillating feature at the crack tip is numerically investigated. Computation of the fracture parameter, i.e., the *J*-integral, using the domain form of the contour integral, is presented. Excellent accuracy of the proposed formulation is demonstrated on benchmark interface crack problems through comparisons with analytical solutions and numerical results obtained by the classical FEM. Moreover, it is shown that the geometrical enrichment combining the mesh with local refinement is substantially better in terms of accuracy and efficiency. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a non-intrusive stochastic model reduction scheme is developed for polynomial chaos representation using proper orthogonal decomposition. The main idea is to extract the optimal orthogonal basis via inexpensive calculations on a coarse mesh and then use them for the fine-scale analysis. To validate the developed reduced-order model, the method is implemented to: (1) the stochastic steady-state heat diffusion in a square slab; (2) the incompressible, two-dimensional laminar boundary-layer over a flat plate with uncertainties in free-stream velocity and physical properties; and (3) the highly nonlinear Ackley function with uncertain coefficients. For the heat diffusion problem, the thermal conductivity of the slab is assumed to be a stochastic field with known exponential covariance function and approximated via the Karhunen–Loève expansion. In all three test cases, the input random parameters are assumed to be uniformly distributed, and a polynomial chaos expansion is found using the regression method. The Sobol's quasi-random sequence is used to generate the sample points. The numerical results of the three test cases show that the non-intrusive model reduction scheme is able to produce satisfactory results for the statistical quantities of interest. It is found that the developed non-intrusive model reduction scheme is computationally more efficient than the classical polynomial chaos expansion for uncertainty quantification of stochastic problems. The performance of the developed scheme becomes more apparent for the problems with larger stochastic dimensions and those requiring higher polynomial order for the stochastic discretization. Copyright © 2015 John Wiley & Sons, Ltd.

Among numerous finite element techniques, few models can perfectly (without any numerical problems) break through MacNeal's theorem: any 4-node, 8-DOF membrane element will either lock in in-plane bending or fail to pass a *C*_{0} patch test when the element's shape is an isosceles trapezoid. In this paper, a 4-node plane quadrilateral membrane element is developed following the unsymmetric formulation concept, which means two different sets of interpolation functions for displacement fields are simultaneously used. The first set employs the shape functions of the traditional 4-node bilinear isoparametric element, while the second set adopts a novel composite coordinate interpolation scheme with analytical trail function method, in which the Cartesian coordinates (*x*,*y*) and the second form of quadrilateral area coordinates (QACM-II) (*S*,*T*) are applied together. The resulting element US-ATFQ4 exhibits amazing performance in rigorous numerical tests. It is insensitive to various serious mesh distortions, free of trapezoidal locking, and can satisfy both the classical first-order patch test and the second-order patch test for pure bending. Furthermore, because of usage of the second form of quadrilateral area coordinates (QACM-II), the new element provides the invariance for the coordinate rotation. It seems that the behaviors of the present model are beyond the well-known contradiction defined by MacNeal's theorem. Copyright © 2015 John Wiley & Sons, Ltd.

An algorithm is derived for the computation of eigenpair derivatives of asymmetric quadratic eigenvalue problem with distinct and repeated eigenvalues. In the proposed method, the eigenvector derivatives of the damped systems are divided into a particular solution and a homogeneous solution. By introducing an additional normalization condition, we construct two extended systems of linear equations with nonsingular coefficient matrices to calculate the particular solution. The method is numerically stable, and the homogeneous solutions are computed by the second-order derivatives of the eigenequations. Two numerical examples are used to illustrate the validity of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

The material-point method models continua by following a set of unconnected material points throughout the deformation of a body. This set of points provides a Lagrangian description of the material and geometry. Information from the material points is projected onto a background grid where equations of motion are solved. The grid solution is then used to update the material points. This paper describes how to use this method to solve quasi-static problems. The resulting discrete equations are a coupled set of nonlinear equations that are then solved with a Jacobian-free, Newton–Krylov algorithm. The technique is illustrated by examining two problems. The first problem simulates a compact tension test and includes a model of material failure. The second problem computes effective, macroscopic properties of a polycrystalline thin film. Copyright © 2015 John Wiley & Sons, Ltd.

A robust computational framework for the solution of fluid–structure interaction problems characterized by compressible flows and highly nonlinear structures undergoing pressure-induced dynamic fracture is presented. This framework is based on the finite volume method with exact Riemann solvers for the solution of multi-material problems. It couples a Eulerian, finite volume-based computational approach for solving flow problems with a Lagrangian, finite element-based computational approach for solving structural dynamics and solid mechanics problems. Most importantly, it enforces the governing fluid–structure transmission conditions by solving local, one-dimensional, fluid–structure Riemann problems at evolving structural interfaces, which are embedded in the fluid mesh. A generic, comprehensive, and yet effective approach for representing a fractured fluid–structure interface is also presented. This approach, which is applicable to several finite element-based fracture methods including inter-element fracture and remeshing techniques, is applied here to incorporate in the proposed framework two different and popular approaches for computational fracture in a seamless manner: the extended FEM and the element deletion method. Finally, the proposed embedded boundary computational framework for the solution of highly nonlinear fluid–structure interaction problems with dynamic fracture is demonstrated for one academic and three realistic applications characterized by detonations, shocks, large pressure, and density jumps across material interfaces, dynamic fracture, flow seepage through narrow cracks, and structural fragmentation. Correlations with experimental results, when available, are also reported and discussed. For all four considered applications, the relative merits of the extended FEM and element deletion method for computational fracture are also contrasted and discussed. Copyright © 2015 John Wiley & Sons, Ltd.

We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off-the-shelf time integrators. We demonstrate the approach by using Taylor-Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge-Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations. Copyright © 2015 John Wiley & Sons, Ltd.

Generating matching meshes for problems with complex boundaries is often an intricate process, and the use of non-matching meshes appears as an appealing solution. Yet, enforcing boundary conditions on non-matching meshes is not a straightforward process, especially when prescribing those of Dirichlet type. By combining a type of Generalized Finite Element Method (GFEM) with the Lagrange multiplier method, a new technique for the treatment of essential boundary conditions on non-matching meshes is introduced in this manuscript. The new formulation yields a symmetric stiffness matrix and is straightforward to implement. As a result, the methodology makes possible the analysis of problems with the use of simple structured meshes, irrespective of the problem domain boundary. Through the solution of linear elastic problems, we show that the optimal rate of convergence is preserved for piecewise linear finite elements. Yet, the formulation is general and thus it can be extended to other elliptic boundary value problems. Copyright © 2015 John Wiley & Sons, Ltd.

A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.

The generalized-*α* method (G*α*) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+*ξ*) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.

The main contribution is to show that the energy–momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+*ξ* with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices. Copyright © 2015 John Wiley & Sons, Ltd.

In discrete element method simulations, multi-sphere particle is extensively employed for modeling the geometry shape of non-spherical particle. A contact detection algorithm for multi-sphere particles has been developed through two-level-grid-searching. In the first-level-grid-searching, each multi-sphere particle is represented by a bounding sphere, and global space is partitioned into identical square or cubic cells of size *D*, the diameter of the greatest bounding sphere. The bounding spheres are mapped into the cells in global space. The candidate particles can be picked out by searching the bounding spheres in the neighbor cells of the bounding sphere for the target particle. In the second-level-grid-searching, a square or cubic local space of size (*D* + *d*) is partitioned into identical cells of size *d*, the diameter of the greatest element sphere. If two bounding spheres of two multi-sphere particles are overlapped, the contacts occurring between the element spheres in the target multi-sphere particle and in the candidate multi-sphere particle are checked. Theoretical analysis and numerical tests on the memory requirement and contact detection time of this algorithm have been performed to verify the efficiency of this algorithm. The results showed that this algorithm can effectively deal with the contact problem for multi-sphere particles. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, the extended finite element method (XFEM) is for the first time coupled with face-based strain-smoothing technique to solve three-dimensional fracture problems. This proposed method, which is called face-based smoothed XFEM here, is expected to combine both the advantages of XFEM and strain-smoothing technique. In XFEM, arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing. Strain-smoothing technique can eliminate the integration of singular term over the volume around the crack front, thanks to the transformation of volume integration into area integration. Special smoothing scheme is implemented in the crack front smoothing domain. Three examples are presented to test the accuracy, efficiency, and convergence rate of the face-based smoothed XFEM. From the results, it is clear that smoothing technique can improve the performance of XFEM for three-dimensional fracture problems. Copyright © 2015 John Wiley & Sons, Ltd.