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

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 (SROMS), and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry are captured by calibrating plasticity parameters to experimental observations of necking as, due to 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 to traditional Monte Carlo simulation with rather remarkable results. This article is protected by copyright. All rights reserved.

A two-scale parameter identification approach is investigated. The microscopic material parameters of a two-scale model are identified by comparing macroscopic simulation data to 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 to 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. 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.

This paper describes a *modified extended finite element* (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. This article is protected by copyright. All rights reserved.

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

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

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

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

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 7-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 6 strain and 6 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. This article is protected by copyright. All rights reserved.

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

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

The extended finite element method (XFEM) 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 (HRR) 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. 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.

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

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.

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.

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.

Predicting the frequency response of a complex vibro-acoustic system becomes extremely difficult in the mid-frequency regime. In this work, a novel hybrid face-based smoothed finite element method/statistical energy analysis (FS-FEM/SEA) method is proposed, aiming to further improve the accuracy of ‘mid-frequency’ predictions. According to this approach, the whole vibro-acoustic system is divided into a combination of a plate subsystem with statistical behaviour and an acoustic cavity subsystem with deterministic behaviour. The plate subsystem is treated using the recently developed FS-FEM, and the cavity subsystem is dealt with using the SEA. These two different types of subsystems can be coupled and interacted through the so-called diffuse field reciprocity relation. The ensemble average response of the system is calculated, and the uncertainty is confined and treated in the SEA subsystems. The use of FS-FEM ‘softens’ the well-known ‘overly stiff’ behaviour in the standard FEM and reduces the inherent numerical dispersion error. The proposed FS-FEM/SEA approach is verified and its features are examined by various numerical examples. 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 hybrid finite element formulation is used to model the hygro-thermo-chemical process of cement hydration in high performance concrete. The temperature and the relative humidity fields are directly approximated in the domain of the element using naturally hierarchical bases independent of the mapping used to define its geometry. This added flexibility in modeling implies the independent approximation of the heat and moisture flux fields on the boundary of the element, the typical feature of hybrid finite element formulations. The formulation can be implemented using coarse and, eventually, unstructured meshes, which may contain elements with high aspect ratios, an option that can be advantageously used in the simulation of the casting of concrete structural elements. The resulting solving system is sparse and well suited to adaptive refinement and parallelization. It is solved coupling a trapezoidal time integration rule with an adaptation of the Newton–Raphson method designed to preserve symmetry. The relative performance of the formulation is assessed using a set of testing problems supported by experimental data and results obtained with conventional (conform) finite elements. Copyright © 2015 John Wiley & Sons, Ltd.

Based on the one-dimensional differential matrix derived from the Lagrange series expansion, the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials. In this paper, the formulation of the Lagrange finite block method with boundary type in the strong form is presented and applied to non-conforming contact problems for the functionally graded materials subjected to either static or dynamic loads. The first order partial differential matrices are only needed both in the governing equations and in the Neumann boundary condition. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate of global system to the normalized coordinate with eight seeds. Time dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin's inversion method is applied to determine all the physical values in the time domain. Conforming and non-conforming contacts are investigated by using the iterative algorithm with full load technique. Illustrative numerical examples are given and comparisons have been made with analytical solutions. Copyright © 2015 John Wiley & Sons, Ltd.

We develop an acceleration method for material-dominated calculations based on phase-space simplicial interpolation of the relevant material-response functions. This process of interpolation constitutes an approximation scheme by which an exact material-response function is replaced by a sequence of approximating response functions. The terms in the sequence are increasingly accurate, thus ensuring the convergence of the overall solution. The acceleration ratio depends on the dimensionality, the complexity of the deformation, the time-step size, and the fineness of the phase-space interpolation. We ascertain these trade-offs analytically and by recourse to selected numerical tests. The numerical examples with piecewise-quadratic interpolation in phase space confirm the analytical estimates. Copyright © 2015 John Wiley & Sons, Ltd.

The properties and numerical performance of reduced-order models based on trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) are assessed. The target application is subsurface flow modeling, although our findings should be applicable to a range of problems. The errors arising at each step in the POD–TPWL procedure are described. The impact of constraint reduction on accuracy and stability is considered in detail. Constraint reduction entails projection of the overdetermined system into a low-dimensional subspace, in which the system is solvable. Optimality conditions for constraint reduction, in terms of error minimization, are derived. Galerkin and Petrov–Galerkin projections are shown to correspond to optimality in norms that involve weighting with the Jacobian matrix. Two new treatments, inverse projection and weighted inverse projection, are suggested. These methods minimize error in appropriate norms, although they require substantial preprocessing computations. Numerical results are presented for oil reservoir simulation problems. Galerkin projection provides reasonable accuracy for simpler oil–water systems, although it becomes unstable in more challenging cases. Petrov–Galerkin projection is observed to behave stably in all cases considered. Weighted inverse projection also behaves stably, and it provides the highest accuracy. Runtime speedups of 150–400 are achieved using these POD–TPWL models. Copyright © 2015 John Wiley & Sons, Ltd.

This paper addresses the problem of finding a stationary point of a nonlinear dynamical system whose state variables are under inequality constraints. Systems of this type often arise from the discretization of PDEs that model physical phenomena (e.g., fluid dynamics) in which the state variables are under realizability constraints (e.g., positive pressure and density). We start from the popular pseudo-transient continuation method and augment it with nonlinear inequality constraints. The constraint handling technique does not help in situations where no steady-state solution exists, for example, because of an under-resolved discretization of PDEs. However, an often overlooked situation is one in which the steady-state solution exists but cannot be reached by the solver, which typically fails because of the violation of constraints, that is, a non-physical state error during state iterations. This is the shortcoming that we address by incorporating physical realizability constraints into the solution path from the initial condition to steady state. Although we focus on the DG method applied to fluid dynamics, our technique relies only on implicit time marching and hence can be extended to other spatial discretizations and other physics problems. We analyze the sensitivity of the method to a range of input parameters and present results for compressible turbulent flows that show that the constrained method is significantly more robust than a standard unconstrained method while on par in terms of cost. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a novel formulation of a hereditary cohesive zone model able to effectively capture rate-dependent crack propagation along a defined interface, over a wide range of applied loading rates and with a single set of seven input parameters only, as testified by the remarkable agreement with experimental results in the case of a double cantilever beam made of steel adherends bonded along a rubber interface. The formulation relies on the assumption that the measured fracture energy is the sum of a rate-independent ‘rupture’ energy, related to the rupture of primary bonds at the atomic or molecular level, and of additional dissipation caused by other rate-dependent dissipative mechanisms present in the material and occurring simultaneously to rupture. The first contribution is accounted for by introducing a damage-type internal variable, whose evolution follows a rate-independent law for consistency with the assumption of rate independence of the rupture energy. To account for the additional dissipation, a fractional-calculus-based linear viscoelastic model is used, because for many polymers, it is known to capture the material response within an extremely wide range of strain rates much more effectively than classic models based on an exponential kernel. To the authors' knowledge, this is the first application of fractional viscoelasticity to the simulation of fracture. © 2015 The Authors. *International Journal for Numerical Methods in Engineering* published by John Wiley & Sons Ltd.

We present a robust method for generating high-order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second, displacing the boundary nodes to ensure that they are on the computer-aided design surface, and third, smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high-order mesh. The smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh. This means that whenever possible, the resulting mesh preserves the geometrical features of the initial linear mesh such as shape, stretching, and size. We present several examples to illustrate the performance of the proposed algorithm. Furthermore, the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements. The meshes obtained are suitable for high-order finite element analyses. Copyright © 2015 John Wiley & Sons, Ltd.

This paper provides a comparison between one particular *phase-field* damage model and a *thick level set* (TLS) damage model for the simulation of brittle and quasi-brittle fractures. The TLS model is recasted in a variational framework, which allows comparison with the phase-field model. Using this framework, both the equilibrium equations and the damage evolution laws are guided by the initial choice of the potential energy. The potentials of the phase-field model and of the TLS model are quite different. TLS potential enforces *a priori* a bound on damage gradient whereas the phase-field potential does not. The TLS damage model is defined such that the damage profile fits to the one of the phase-field model for a beam of infinite length. The model parameters are calibrated to obtain the same surface fracture energy. Numerical results are provided for unidimensional and bidimensional tests for both models. Qualitatively, similar results are observed, although TLS model is observed to be less sensible to boundary conditions. Copyright © 2015 John Wiley & Sons, Ltd.

A new numerical approach for solving incompressible two-phase flows is presented in the framework of the recently developed Consistent Particle Method (CPM). In the context of the Lagrangian particle formulation, the CPM computes spatial derivatives based on the generalized finite difference scheme and produces good results for single-phase flow problems. Nevertheless, for two-phase flows, the method cannot be directly applied near the fluid interface because of the abrupt discontinuity of fluid density resulting in large change in pressure gradient. This problem is resolved by dealing with the pressure gradient normalized by density, leading to a two-phase CPM of which the original singlephase CPM is a special case. In addition, a new adaptive particle selection scheme is proposed to overcome the problem of ill-conditioned coefficient matrix of pressure Poisson equation when particles are sparse and non-uniformly spaced. Numerical examples of Rayleigh–Taylor instability, gravity current flow, water-air sloshing and dam break are presented to demonstrate the accuracy of the proposed method in wave profile and pressure solution. 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.

The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving embedded interface problems. With a few exceptions, the X-FEM has mostly been used in conjunction with piecewise-linear shape functions and an associated piecewise-linear geometrical representation of interfaces. In the current work, the use of spline-based finite elements is examined along with a Nitsche technique for enforcing constraints on an embedded interface. To obtain optimal rates of convergence, we employ a hierarchical local refinement approach to improve the geometrical representation of curved interfaces. We further propose a novel weighting for the interfacial consistency terms arising in the Nitsche variational form with B-splines. A qualitative dependence between the weights and the stabilization parameters is established with additional element level eigenvalue calculations. An important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of large heterogeneities as well as elements with arbitrarily small volume fractions. We demonstrate the accuracy and robustness of the proposed method through several numerical examples. 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.

Non-probabilistic *convex models* need to be provided only the changing boundary of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is lacking. The *interval* and the *ellipsoidal models* are the two most commonly used modeling methods in the field of non-probabilistic convex modeling. However, the former can only deal with independent variables, while the latter can only deal with dependent variables. This paper presents a more general non-probabilistic convex model, the *multidimensional parallelepiped model*. This model can include the independent and dependent uncertain variables in a unified framework and can effectively deal with complex ‘multi-source uncertainty’ problems in which dependent variables and independent variables coexist. For any two parameters, the concepts of the correlation angle and the correlation coefficient are defined. Through the marginal intervals of all the parameters and also their correlation coefficients, a multidimensional parallelepiped can easily be built as the uncertainty domain for parameters. Through the introduction of affine coordinates, the parallelepiped model in the original parameter space is converted to an interval model in the affine space, thus greatly facilitating subsequent structural uncertainty analysis. The parallelepiped model is applied to structural uncertainty propagation analysis, and the response interval of the structure is obtained in the case of uncertain initial parameters. Finally, the method described in this paper was applied to several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

The vector potential formulation is a promising solution method for nonlinear electromechanically coupled boundary value problems. However, one of the drawbacks of this formulation is the non-uniqueness of the (electric) vector potential in three dimensions. The present paper focuses on the Coulomb gauging method to overcome this problem. In particular, the corresponding gauging boundary conditions and their consistency with the physical boundary conditions are examined in detail. Furthermore, certain topological features like cavities and multiply connectedness of the domain of analysis are taken into account. Different variational/weak formulations being appropriate for finite element implementation are described. Finally, the suitability of these formulations is demonstrated in several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Zero-thickness interface elements are commonly used in computational mechanics to model material interfaces or to introduce discontinuities. The latter class requires the existence of a non-compliant interface prior to the onset of fracture initiation. This is accomplished by assigning a high dummy stiffness to the interface prior to cracking. This dummy stiffness is known to introduce oscillations in the traction profile when using Gauss quadrature for the interface elements, but these oscillations are removed when resorting to a Newton-Cotes integration scheme 1. The traction oscillations are aggravated for interface elements that use B-splines or non-uniform rational B-splines as basis functions (isogeometric interface elements), and worse, do not disappear when using Newton-Cotes quadrature. An analysis is presented of this phenomenon, including eigenvalue analyses, and it appears that the use of lumped integration (at the control points) is the only way to avoid the oscillations in isogeometric interface elements. New findings have also been obtained for standard interface elements, for example that oscillations occur in the relative displacements at the interface irrespective of the value of the dummy stiffness. Copyright © 2015 John Wiley & Sons, Ltd.

A strategy for a two-dimensional contact analysis involving finite strain plasticity is developed with the aid of variable-node elements. The variable-node elements, in which nodes are added freely where they are needed, make it possible to transform the non-matching meshes into matching meshes directly. They thereby facilitate an efficient analysis, maintaining node-to-node contact during the contact deformation. The contact patch test, wherein the contact patch is constructed out of variable-node elements, is thus passed, and iterations for equilibrium solutions reach convergence faster in this scheme than in the conventional approach based on the node-to-surface contact. The effectiveness and accuracy of the proposed scheme are demonstrated through several numerical examples of elasto-plastic contact analyses. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, a new, unconditionally stable, time marching procedure for dynamic analyses is presented. The scheme is derived from the standard central difference approximation, with stabilization being provided by a consistent perturbation of the original problem. Because the method only involves constitutive variables that are already available from computations at previous time steps, iterative procedures are not required to establish equilibrium when nonlinear models are focused, allowing more efficient analyses to be obtained. The theoretical properties of the proposed scheme are discussed taking into account standard stability and accuracy analyses, indicating the excellent performance of the new technique. At the end of the contribution, representative nonlinear numerical examples are studied, further illustrating the effectiveness of the new technique. Numerical results obtained by the standard central difference procedure and the implicit constant average acceleration method are also presented along the text for comparison. Copyright © 2015 John Wiley & Sons, Ltd.

Recently, graphics processing units (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector (SPMV) multiplication operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis and also show that the proposed algorithms can yield speedup factors up to 12-fold for real finite element applications. Copyright © 2015 John Wiley & Sons, Ltd.

A time-domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields. The proposed numerical algorithm is a modification of the radial point interpolation method, where radial basis functions are used for local interpolation of the vector potentials and their derivatives. In the proposed implementation, solving the second-order vector potential wave equation intrinsically enforces the divergence-free property of the electric and magnetic fields. Furthermore, the computational effort associated with the generation of a dual node distribution (as required for solving the first-order Maxwell's equations) is avoided. The proposed method is validated with several examples of 2D waveguides and filters, and the convergence is empirically demonstrated in terms of node density or size of local support domains. It is further shown that inhomogeneous node distributions can provide increased convergence rates, that is, the same accuracy with smaller number of nodes compared with a solution for homogeneous node distribution. A comparison of the magnetic vector potential technique with conventional radial point interpolation method is performed, highlighting the superiority of the divergence-free formulation. Copyright © 2015 John Wiley & Sons, Ltd.

We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically. © 2014 The Authors. *International Journal for Numerical Methods in Engineering* published by John Wiley & Sons Ltd.

An efficient procedure for embedding kinematic boundary conditions in the biharmonic equation, for problems such as the pure streamfunction formulation of the Navier–Stokes equations and thin plate bending, is based on a stabilized variational formulation, obtained by Nitsche's approach for enforcing boundary constraints. The absence of kinematic admissibility constraints allows the use of non-conforming meshes with non-interpolatory approximations, thereby providing added flexibility in addressing the higher continuity requirements typical of these problems. Variationally conjugate pairs weakly enforce kinematic boundary conditions. The use of a scaling factor leads to a formulation with a single stabilization parameter. For plates, the enforcement of tangential derivatives of deflections obviates the need for pointwise enforcement of corner values in the presence of corners. The single stabilization parameter is determined from a local generalized eigenvalue problem, guaranteeing coercivity of the discrete bilinear form. The accuracy of the approach is verified by representative computations with bicubic B-splines, providing guidance to the determination of the scaling and exhibiting optimal rates of convergence and robust performance with respect to values of the stabilization parameter. Copyright © 2014 John Wiley & Sons, Ltd.

In this work, we propose a method to prescribe essential boundary conditions in the finite element approximation of elliptic problems when the boundary of the computational domain does not match with the element boundaries. The problems considered are the Poisson problem, the Stokes problem, and the Darcy problem, the latter both in the primal and in the dual formulation. The formulation proposed is of variational type. The key idea is to start with the variational form that defines the problem and treat the boundary condition as a constraint. The particular feature is that the Lagrange multiplier is not defined on the boundary where the essential condition needs to be prescribed but is taken as a certain trace of a field defined in the computational domain, either in all of it or just in a region surrounding the boundary. When approximated numerically, this may allow one to condense the DOFs of the new field and end up with a problem posed only in terms of the original unknowns. The nature of the field used to weakly impose boundary conditions depends on the problem being treated. For the Poisson problem, it is a flux; for the Stokes problem, a stress; for the Darcy problem in primal form, a velocity field; and for the Darcy problem in dual form, it is a potential. Copyright © 2014 John Wiley & Sons, Ltd.

A novel extended variational multiscale method for incompressible two-phase flow is proposed. In this approach, the level-set method, which allows for accurately representing complex interface evolutions, is combined with an extended finite element method for the fluid field. Sharp representation of the discontinuities at the interface related to surface-tension effects and large material–parameter ratios are enabled by this approach. To capture the discontinuities, jump enrichments are applied for both velocity and pressure field. Nitsche's method is then used to weakly impose the continuity of the velocity field. For a stable formulation on the entire domain, residual-based variational multiscale terms are supported by appropriate face-oriented ghost-penalty and fluid stabilization terms in the region of enriched elements. Both face-oriented terms and interfacial terms related to Nitsche's method are introduced such that it is accounted for viscous-dominated and convection-dominated transient flows. As a result, stability and well-conditioned systems are guaranteed independent of the interface location. The proposed method is applied to four numerical examples of increasing complexity: two-dimensional Rayleigh–Taylor instabilities, a two-dimensional collapsing water column, three-dimensional rising bubbles, and a three-dimensional bubble coalescence. Excellent agreement with either analytical solutions or numerical and experimental reference data as well as robustness for all flow regimes is demonstrated for all examples. Copyright © 2014 John Wiley & Sons, Ltd.

An embedded mesh method using piecewise constant multipliers originally proposed by Puso *et al.* (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Next, it is shown that the constraints and the stabilization terms can be recast as non-proportional damping such that the time integration of the scheme is provably stable with a critical time step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, several demanding problems highlighting the robustness of the proposed approach are shown. Copyright © 2014 John Wiley & Sons, Ltd.

Dielectric materials like electro-active polymers (EAPs) exhibit coupled electro-mechanical behavior at large strains. They respond by a deformation to an applied electrical field and are used in advanced industrial environments as sensors and actuators, for example, in robotics, biomimetics and smart structures. In field-activated or electronic EAPs, the electric activation is driven by Coulomb-type electrostatic forces, resulting in Maxwell stresses. These materials are able to provide finite actuation strains, which can even be improved by optimizing their composite microstructure. However, EAPs suffer from different types of instabilities. This concerns *global structural instabilities*, such as buckling and wrinkling of EAP devices, as well as *local material instabilities*, such as limit-points and bifurcation-points in the constitutive response, which induce snap-through and fine scale localization of local states. In this work, we outline variational-based definitions for structural and material stability, and design algorithms for accompanying stability checks in typical finite element computations. The formulation starts from stability criteria for a *canonical energy minimization principle* of electro-elasto-statics, and then shifts them over to representations related to an *enthalpy-based saddle point principle* that is considered as the most convenient setting for numerical implementation. Here, global structural stability is analyzed based on a *perturbation of the total electro-mechanical energy*, and related to statements of positive definiteness of incremental finite element tangent arrays. We base the local material stability on an *incremental quasi-convexity condition* of the electro-mechanical energy, inducing the positive definiteness of both the incremental electro-mechanical moduli as well as a generalized acoustic tensor. It is shown that the incremental arrays to be analyzed in the stability criteria appear within the enthalpy-based setting in a *distinct diagonal form*, with pure mechanical and pure electrical partitions. Applications of accompanying stability analyses in finite element computations are demonstrated by means of representative model problems. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical techniques are suggested in this paper, in order to improve the computational efficiency of the spectral boundary integral method, initiated by Clamond & Grue [D. Clamond and J. Grue. A fast method for fully nonlinear water-wave computations. *J*. *Fluid Mech*. 2001; **447**: 337–355] for simulating nonlinear water waves. This method involves dealing with the high order convolutions by using Fourier transform or inverse Fourier transform and evaluating the integrals with weakly singular integrands. A de-singularity technique is proposed here to help in efficiently evaluating the integrals with weak singularity. An anti-aliasing technique is developed in this paper to overcome the aliasing problem associated with Fourier transform or inverse Fourier transform with a limited resolution. This paper also presents a technique for determining a critical value of the free surface, under which the integrals can be neglected. Numerical tests are carried out on the numerical techniques and on the improved method equipped with the techniques. The tests will demonstrate that the improved method can significantly accelerate the computation, in particular when waves are strongly nonlinear. Copyright © 2015 John Wiley & Sons, Ltd.

The computational burden associated to finite element based digital image correlation methods is mostly due to the inversion of finite element systems and to image interpolations. A non-overlapping dual domain decomposition method is here proposed to rationalise the computational cost of high resolution finite element digital image correlation measurements when dealing with large images. It consists in splitting the global mesh into submeshes and the reference and deformed states images into subset images. Classic finite element digital image correlation formulations are first written in each subdomain independently. The displacement continuity at the interfaces is enforced by introducing a set of Lagrange multipliers. The problem is then condensed on the interface and solved by a conjugate gradient algorithm. Three different preconditioners are proposed to accelerate its convergence. The proposed domain decomposition method is here exemplified with real high resolution images. It is shown to combine the metrological performances of finite element based digital image correlation and the parallelisation ability of subset based methods. Copyright © 2015 John Wiley & Sons, Ltd.