A major challenge for crash failure analysis of laminated composites is to find a modelling approach which is both sufficiently accurate, e.g. able to capture delaminations, and computationally efficient to allow full scale vehicle crash simulations.

Addressing this challenge, we propose a methodology based on an equivalent single-layer shell formulation which is adaptively through-the-thickness refined to capture initiating and propagating delaminations. To be specific, single shell elements through the laminate thickness are locally and adaptively enriched using the XFEM such that delaminations can be explicitly modelled without having to be represented by separate elements. Furthermore, the shell formulation is combined with a stress recovery technique which increase the accuracy of predicting delamination initiations.

The paper focuses on the parameters associated with identifying, introducing and extending the enrichment areas; especially on the impact of these parameters on the resulting structural deformation behaviour. We conclude that the delamination enrichment must be large enough to allow the fracture process to be accurately resolved and we propose a suitable approach to achieve this. The proposed methodology for adaptive delamination modelling shows potential for being computationally efficient and, thereby, it has the potential to enable efficient and accurate full vehicle crash simulations of laminated composites. This article is protected by copyright. All rights reserved.

This paper introduces a hierarchical sequential arbitrary Lagrangian-Eulerian (ALE) model for predicting the tire-soil-water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two-phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium are idealized as hyperelastic. Meanwhile, the interaction between tire, soil and water will be simulated via a hierarchical operator-split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire-soil-water interaction both close to the contact and in the far field. The presented ALE model for tire-soil-water interaction provides the essential basis for future applications e.g. to a path-dependent frictional-cohesive response of the consolidating soil and unsaturated soil, respectively. This article is protected by copyright. All rights reserved.

A reduction/hyper reduction framework is presented for dramatically accelerating the solution of nonlinear dynamic multiscale problems in structural and solid mechanics. At each scale, the dimensionality of the governing equations is reduced using the method of snapshots for Proper Orthogonal Decomposition (POD), and computational efficiency is achieved for the evaluation of the nonlinear reduced-order terms using a carefully designed configuration of the Energy Conserving Sampling and Weighting (ECSW) method. Periodic boundary conditions at the microscales are treated as linear multipoint constraints and reduced via projection onto the span of a basis formed from the singular value decomposition of Lagrange multiplier snapshots. Most importantly, information is efficiently transmitted between the scales without incurring high-dimensional operations. In this proposed POD-ECSW nonlinear model reduction framework, training is performed in two steps. First, a microscale hyper reduced-order model is constructed *in-situ*, or using a mesh coarsening strategy, in order to achieve significant speedups even in non-parametric settings. Next, a classical offline-online training approach is performed to build a parametric hyper reduced-order macroscale model, which completes the construction of a fully hyper reduced-order parametric multiscale model capable of fast and accurate multiscale simulations. A notable feature of this computational framework is the minimization, at the macroscale level, of the cost of the offline training using the *in-situ* or coarsely-trained hyper reduced-order microscale model to accelerate snapshot acquisition. The effectiveness of the proposed hyper reduction framework at accelerating the solution of nonlinear dynamic multiscale problems is demonstrated for two problems in structural and solid mechanics. Speedup factors as high as five orders of magnitude are shown to be achievable. This article is protected by copyright. All rights reserved.

We introduce a new cell-centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and flow in porous media, and falls in the category of multi-point stress approximations (MPSA). By enforcing symmetry weakly, the resulting method has flexibility beyond previous MPSA methods. This allows for a construction of a method which is applicable to simplexes, quadrilaterals and most planar-faced polyhedral grids in both 2D and 3D, and in particular the method amends a convergence failure in previous MPSA methods for certain simplex grids.

We prove convergence of the new method for a wide range of problems, with conditions that can be verified at the time of discretization. We present the first set of comprehensive numerical tests for the MPSA methods in three dimensions, covering Cartesian and simplex grids, with both heterogeneous and nearly incompressible media. The tests show that the new method consistently is second order convergent in displacement, despite being lowest order, with a rate that mostly is between 1 and 2 for stresses. The results further show that the new method is more robust and computationally cheaper than previous MPSA methods.

The scaled boundary radial point interpolation method (SBRPIM), a new semi-analytical technique, is introduced and applied to the analysis of the stress-strain problems. The proposed method combines the advantages of the scaled boundary finite element method (SBFEM) and the boundary radial point interpolation method (BRPIM). In this method no mesh is required, nodes are scattered only on the boundary of the domain, no fundamental solution is required and as the shape functions constructed based on the radial point interpolation method (RPIM) possess the Kronecker delta function property, the boundary conditions of problems can be imposed accurately without additional efforts. The main ideas of the SBRPIM are introducing a new method based on boundary scattered nodes without the need to element connectivity information, satisfying Kronecker delta function property and capable to handle singular problems. The equations of the SBRPIM in stress-strain fields are outlined in this paper. Several benchmark examples of 2D elastostatic are analyzed to validate the accuracy and efficiency of the proposed method. It is found that the SBRPIM are very easy to implement and the obtained results of the proposed method show a very good agreement with the analytical solution.

The numerical manifold method (NMM) builds up a unified framework that is used to describe continuous and discontinuous problems; it is an attractive method for simulating a cracking phenomenon. Taking into account the differences between the generalized degrees of freedom of the physical patch and nodal displacement of the element in the NMM, a decomposition technique of generalized degrees of freedom is deduced for mixed mode crack problems. An analytic expression of the energy release rate, which is caused by a virtual crack extension technique (VCET), is proposed. The necessity of using a symmetric mesh is demonstrated in detail by analysing an additional error that had previously been overlooked. Because of this necessity, the local mathematical cover refinement is further applied. Finally, four comparison tests are given to illustrate the validity and practicality of the proposed method. The abovementioned aspects are all implemented in the high-order NMM, so this study can be regarded as the development of the VCET and can also be seen as a prelude to an h-version high-order NMM.

We present the theory of novel time-stepping algorithms for general non-linear, non-smooth, coupled, thermomechanical problems. The proposed methods are thermodynamically consistent in the sense that their solutions rigorously comply with the two laws of thermodynamics: for isolated systems they preserve the total energy and the entropy never decreases. Extending previous works on the subject, the newly proposed integrators are applicable to coupled mechanical systems with non-smooth kinetics and can be formulated in arbitrary variables. The ideas are illustrated with a simple non-smooth problem: a rheological model for a thermo-elasto-plastic material with hardening. Numerical simultions verify the qualitative features of the proposed methods and illustrate their excellent numerical stability, which stems precisely from their ability to preserve the structure of the evolution equations they discretize. This article is protected by copyright. All rights reserved.

A novel density-based topology optimization framework for plastic energy absorbing structural designs with maximum damage constraint is proposed. This framework enables topologies to absorb large amount of energy via plastic work before failure occurs. To account for the plasticity and damage during the energy absorption, a coupled elastoplastic ductile damage model is incorporated with topology optimization. Appropriate material interpolation schemes are proposed to relax the damage in the low-density regions while still ensuring the convergence of Newton-Raphson solution process in the nonlinear finite element analyses. An effective method for obtaining path-dependent sensitivities of the plastic work and maximum damage via adjoint method is presented, and the sensitivities are verified by the central difference method. The effectiveness of the proposed methodology is demonstrated through a series of numerical examples.

Various reduced basis element (RBE) methods are compared for performing transient thermal simulations of integrated circuits (ICs). The RBE method is a type of reduced order modeling that takes advantage of repeated geometrical features. It uses a reduced set of basis functions to approximate the solution of a PDE on subdomains (blocks) then these blocks are coupled together to perform a simulation on an entire domain. As the simulations are transient, a proper-orthogonal-decomposition (POD) basis is used, and the POD eigenvalues from each block are used to derive error bounds for the entire simulation. This bounds is used to examine choices of block decompositions for a simplified IC structure. A decomposition that uses a single block for each transistor device is compared to a decomposition that uses one block for multiple devices. It was found that larger blocks are more computationally efficient; however the advantage decreases if the devices within a block receive independent signals. Continuous and discontinuous methods of coupling the blocks were also compared. The coupling methods lend themselves to different solution approaches such as static condensation (continuous coupling) and block-based inversion (discontinuous). Static condensation yielded the best convergence rate, accuracy, and operation count. This article is protected by copyright. All rights reserved.

Numerical integration techniques are commonly employed to formulate the system matrices encountered in the analysis of variable stiffness beams and plates using a Ritz based approach. Computing these integrals accurately is often computationally costly. Herein, a novel alternative is presented, the Recursive Analytical Polynomial Integral Definition (RAPID) formulation. The RAPID formulation offers a significant improvement in the speed of analysis, achieved by reducing the number of numerical integrations that are performed by an order of magnitude. A common Legendre Polynomial (LP) basis is employed for both trial functions and stiffness/load variations leading to a common form for the integrals encountered. The LP basis possesses algebraic recursion relations that allow these integrals to be reformulated as triple-products with known analytical solutions, defined compactly using the Wigner (3*j*) coefficient. The satisfaction of boundary conditions, calculation of derivatives, and transformation to other bases is achieved through combinations of matrix multiplication, with each matrix representing a unique boundary condition or physical effect, therefore permitting application of the RAPID approach to a variety of problems. Indicative performance studies demonstrate the advantage of the RAPID formulation when compared to direct analysis using MATLAB's “integral” and “integral2”. This article is protected by copyright. All rights reserved.

We propose mixed hybrid finite element formulations for the Stokes problem characterized by the introduction of Lagrange multipliers associated with the traces of the velocity and pressure fields on the edges of the elements to weakly impose the transmission conditions. Both velocity and pressure multipliers are stabilized and, as a consequence of these stabilizations, we prove existence and uniqueness of solution for the local problems. All velocity and pressure degrees-of-freedom can be eliminated at the element level by static condensation leading to a global problem in the multipliers only. The proposed methodology is able to recover stability of very convenient choices of finite element spaces, such as those adopting equal order polynomial approximations for all fields. Numerical experiments illustrate the flexibility and robustness of the proposed formulations and show optimal rates of convergence. This article is protected by copyright. All rights reserved.

Advances in non-destructive material characterization are providing a wealth of information that could be exploited to gain insight into general aspects of material performance, and, in particular, discover relationships between microstructure and thermo-mechanical properties in polycrystalline and other complex composite materials. In order to facilitate the integration of such measurements into existing models, as well as inform new physics-based predictions, we developed a C++/MPI computational framework for sensitivity analysis and parameter estimation. The framework utilizes a micro-mechanical modeling based on Fast Fourier Transforms, direct and adjoint formulations and Markov Chain Monte Carlo sampling techniques. We illustrate the characteristics of this framework and demonstrate its utility by computing the residual stresses arising from thermal expansion of an elastic composite and using data from simulated experiments. We show that the availability of non-destructive 3-D measurements is crucial to reduce the uncertainty in predictions, emphasizing the importance of an integrated experimental/modeling/data analysis approach for improved material characterization and design. This article is protected by copyright. All rights reserved.

The dynamic problem of wave propagation in infinite fluid-saturated porous media is usually solved using the finite element method. Therefore, proper artificial-boundary conditions are required to be imposed on the truncated boundaries of the dynamic finite-element model to consider the radiation damping effect of the truncated media. A local artificial-boundary condition is proposed for the dynamic problems in fluid-saturated porous media in the * u-p* formulation. It avoids making the unrealistic assumption of zero permeability that is widely used in the existing artificial-boundary conditions. Moreover, the proposed method can be implemented easily into finite element or finite difference codes as stress and flow velocity boundary conditions. Numerical results obtained from the finite element model using the proposed artificial boundary indicate that the proposed method is stable for long time and is more accurate than several existing methods.

We present a linearization scheme for an interior penalty discontinuous Galerkin method for two phase porous media flow model which includes dynamic effects in the capillary pressure. The fluids are assumed immiscible and incompressible, and the solid matrix nondeformable. The physical laws are approximated in their original form, without using the global or complementary pressures. The linearization scheme does not require any regularization step. Furthermore, in contrast with Newton or Picard methods, there is no computation of derivatives involved. We prove rigorously that the scheme is robust and linearly convergent. We make an extensive parameter study to compare the behaviour of the L-scheme with the Newton method. This article is protected by copyright. All rights reserved.

This work gives new statement of the vertex solution theorem for exact bounds of the solution to linear interval equations and its novel proof by virtue of the convex set theory. The core idea of the theorem is to transform linear interval equations into a series of equivalent deterministic linear equations. Then, the important theorem is extended to find the upper and lower bounds of static displacements of structures with interval parameters. Following discussions about the computational efforts, a coupled framework based on vertex method (VM) is established, which allows us to solve many large-scale engineering problems with uncertainties using deterministic finite element (FE) software. Compared with the previous works, the contribution of this work is not only to obtain the exact bounds of static displacements, but also lay the foundation for development of an easy-to-use interval FE software. Numerical examples demonstrate the good accuracy of VM. Meanwhile, the implementation of VM and availability of the coupled framework are demonstrated by engineering example.

This study proposed geometrically nonlinear quadratic solid/solid-shell elements applicable for moving structures. Coordinates in the corotational (CR) formulation were established for a solid element. The proposed CR formulation was consistent with other hexahedral or tetrahedral solid type finite elements. The study involved an explicit description of relevant quantities induced during the derivation. Centrifugal and inertial terms were derived to analyze the behavior of moving structures. The formulation derived in the study was applicable for various solid type elements. Thus, an assumed-strain 18-node solid-shell element was developed based on the Hellinger-Reissner principle to avoid locking in the local element. In addition, quadratic solid elements (i.e., a 10-node tetrahedron and a 20-node hexahedron) were developed in the CR solid formulation. Finally, the results were compared with those derived by previous researches involving typical static benchmark problems and commercial software. The findings indicated that a good agreement between the comparisons and validated the proposed finite elements. This article is protected by copyright. All rights reserved.

Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree method are smooth (nonpolynomial functions), and they do not rely on an underlying mesh structure for their construction. These features render meshfree methods to be particularly appealing for higher-order PDEs and for large deformation simulations of solid continua. However, a deficiency that still persists in meshfree Galerkin methods is the inaccuracies in numerical integration, which affects the consistency and stability of the method. Several previous contributions have tackled the issue of integration errors with an eye on consistency, but without explicitly ensuring stability. In this paper, we draw on the recently proposed virtual element method, to present a formulation that guarantees both the consistency and stability of the approximate bilinear form. We adopt maximum-entropy meshfree basis functions, but other meshfree basis functions can also be used within this framework. Numerical results for several two- and three-dimensional elliptic (Poisson and linear elastostatic) boundary-value problems that demonstrate the effectiveness of the proposed formulation are presented. This article is protected by copyright. All rights reserved.

Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso-structures of materials such as 3D-printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non-locality, large deformations, and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering-scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy-consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes, and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem. This article is protected by copyright. All rights reserved.

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. Our approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection-diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes. This article is protected by copyright. All rights reserved.

Linear elasticity problems posed on cracked domains, or domains with re-entrant corners, yield singular solutions that deteriorate the optimality of convergence of finite element methods. In this work, we propose an optimally convergent finite element method for this class of problems. The method is based on approximating a much smoother function obtained by locally reparameterizing the solution around the singularities. This reparameterized solution can be approximated using standard finite element procedures yielding optimal convergence rates for any order of interpolating polynomials, without additional degrees of freedom or special shape functions. Hence the method provides optimally convergent solutions for the same computational complexity of standard finite element methods. Furthermore, the sparsity and the conditioning of the resulting system are preserved. The method handles body forces and crack-face tractions, as well as multiple crack tips and re-entrant corners. The advantages of the method are showcased for four different problems: a straight crack with loaded faces, a circular arc crack, an L-shaped domain undergoing anti-plane deformation, and lastly a crack along a bimaterial interface. Optimality in convergence is observed for all the examples. A proof of optimal convergence is accomplished mainly by proving the regularity of the reparameterized solution. This article is protected by copyright. All rights reserved.

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the Fast Fourier Transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to non-linear problems conceptually difficult. This paper aims to establish a link between FE- and FFT-based methods, in order to develop a solver applicable to general history- and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of non-linear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus needed. By analyzing a two-phase laminate with non-linear elastic, elasto-plastic, and visco-plastic phases, and by elasto-plastic simulations of a dual-phase steel microstructure, we demonstrate that the solver exhibits robust convergence. These results are achieved by re-using the non-linear FE technology, with the potential of further extensions beyond small-strain inelasticity considered in this paper. This article is protected by copyright. All rights reserved.

A mixture theory based model for multi-constituent solids is presented where each constituent is governed by its own balance laws and constitutive equations. Interactive forces between constituents that emanate from maximization of entropy production inequality provide the coupling between constituent specific balance laws and constitutive models. The deformation of multi-constituent mixtures at the Neumann boundaries requires imposing inter-constituent coupling constraints such that the constituents deform in a self-consistent fashion. A set of boundary conditions is presented that accounts for the non-zero applied tractions, and a variationally consistent method is developed to enforce inter constituent constraints at Neumann boundaries in the finite deformation context. The new method finds roots in a local multiscale decomposition of the deformation map at the Neumann boundary. Locally satisfying the Lagrange multiplier field and subsequent modeling of the fine scales via edge bubble functions results in closed-form expressions for a generalized penalty tensor and a weighted numerical flux that are free from tunable parameters. The key novelty is that the consistently derived constituent coupling parameters evolve with material and geometric nonlinearity, thereby resulting in optimal enforcement of inter-constituent constraints. Various benchmark problems are presented to validate the method and show its range of application.

A finite element method is developed to solve a class of integro-differential equations and demonstrated for the important specific problem of non-Fickian contaminant transport in disordered porous media. This transient transport equation, derived from a continuous time random walk approach, includes a memory function. An integral element is the incorporation of the well-known sum-of-exponential approximation of the kernel function, which allows a simple recurrence relation rather than storage of the entire history. A two-dimensional linear element is implemented, including a streamline upwind Petrov–Galerkin weighting scheme. The developed solver is compared with an analytical solution in the Laplace domain, transformed numerically to the time domain, followed by a concise convergence assessment. The analysis shows the power and potential of the method developed here. Copyright © 2017 John Wiley & Sons, Ltd.

The boundary condition represented by polygons in the moving particle semi-implicit method can accurately represent geometries and treat complex geometry with high efficiency. However, inaccurate wall contribution to the Poisson's equation leads to drastic numerical oscillation. To address this issue, in this research, we analyzed the problems of the Poisson's equation used in the boundary condition represented by polygons. The new Poisson's equation is proposed based on the improved source term (Tanaka and Masunaga, Trans Jpn Soc Comput Eng Sci, 2008). The asymmetric gradient model (Khayyer and Gotoh, Coastal Engineering Journal, 2008) is also adopted to further suppress the numerical oscillation of fluid particles. The proposed method can dramatically improve the pressure distribution to arbitrary geometry in three dimensions and keep the efficiency. Four examples including the hydrostatic simulation, dam break simulation, and two complex geometries are verified to show the general applicability of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

Multiphysics simulations are used to solve coupled physics problems found in a wide variety of applications in natural and engineering systems. Combining models of different physical processes into one computational tool is the essence of multiphysics simulation. A general and widely used coupling approach is to combine several ‘single-physics’ numerical solvers, each already being well developed, mature/sophisticated into an iteration-based computational package. This approach iterates over the constituent solvers at every time step, to obtain globally converged solutions. During the simulation, each single-physics component is solved repeatedly until the feedback has been adequately resolved. However, the component problem solution only needs to be as precise as the feedback that it receives from the other component. Thus, computational effort expended to exceed such precision is wasted. This issue is usually called over-solving. This paper proposes and discusses several methods that circumvent over-solving. The residual balance, relaxed relative tolerance, alternating nonlinear, and solution interruption methods are described, and their performance is compared with Picard iteration. A steady state problem with coupling along an interface and a transient problem with two fields coupled throughout the spatial domain are solved as examples. These problems demonstrate that the savings associated with eliminating over-solving can reach at least 30% without any loss in accuracy. Copyright © 2017 John Wiley & Sons, Ltd.

A true integration-free meshless method based on Taylor series named Taylor meshless method (TMM) has been proposed to solve two-dimensional partial differential equations (PDEs). In this framework, the shape functions are approximated solutions of the PDE, and the discretization concerns only the boundary. In this paper, the applicability of TMM to solve large-scale problems is discussed under two aspects. First, as in some other meshless methods, ill-conditioned matrices and round-off error propagation could lead to a loss of accuracy when the number of unknowns increases. This point will be investigated in the case of large-scale problems. Second, the computation time and its distribution are analyzed from numerical experiments for PDEs in a 3D domain. It is established that the TMM method is efficient and robust, even in the case of large-scale problems, while the finite element numerical model involves more than 3 million degrees of freedom. Copyright © 2017 John Wiley & Sons, Ltd.

For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effective hybrid displacement function (HDF) finite element method was successfully developed for solving such difficulty . Although good performances can be obtained in most cases, the distribution continuity of some resulting resultants is destroyed when coarse meshes are employed. Moreover, an additional local coordinate system must be used for avoiding a singular problem in matrix inversion, which makes the derivations more complicated. Based on a modified complementary energy functional containing Lagrangian multipliers, an improved HDF (IHDF) element scheme is proposed in this work. And two new special IHDF elements, named by IHDF-P4-Free and IHDF-P4-SS1, are constructed for modeling plate behaviors near free and soft simply supported boundaries, respectively. The present modeling scheme not only greatly improves the precision of the numerical results but also avoids usage of the additional local Coordinate system. The numerical tests demonstrate that the new IHDF element scheme is an effective way for solving the challenging edge effect problem in Mindlin–Reissner plates. Copyright © 2016 John Wiley & Sons, Ltd.

Volume boundary layer mesh generation on non-smooth geometries with multiple normals is considered in this work. A new highlight is given to corner and ridge boundary layer mesh generation through the generalized Voronoi diagram in general, and the spherical Voronoi diagram in particular. This provides the keystone to allow for the first time boundary layer mesh generation at arbitrary corner configurations. The work proposed in is revisited and compared with the new approach. A detailed description of the new algorithm is provided. The spherical Voronoi diagram delivers geometrically the optimal normals as well as topologically the optimal connectivities, as far as normality is concerned. Numerical examples illustrate the accuracy and robustness of the method. This approach seems to handle arbitrary geometry boundary layer mesh generation, in theory as well as in practice. Copyright © 2017 John Wiley & Sons, Ltd.

Multi-scale problems are often solved by decomposing the problem domain into multiple subdomains, solving them independently using different levels of spatial and temporal refinement, and coupling the subdomain solutions back to obtain the global solution. Most commonly, finite elements are used for spatial discretization, and finite difference time stepping is used for time integration. Given a finite element mesh for the global problem domain, the number of possible decompositions into subdomains and the possible choices for associated time steps is exponentially large, and the computational costs associated with different decompositions can vary by orders of magnitude. The problem of finding an optimal decomposition and the associated time discretization that minimizes computational costs while maintaining accuracy is nontrivial. Existing mesh partitioning tools, such as METIS, overlook the constraints posed by multi-scale methods and lead to suboptimal partitions with a high performance penalty. We present a multi-level mesh partitioning approach that exploits domain-specific knowledge of multi-scale methods to produce nearly optimal mesh partitions and associated time steps automatically. Results show that for multi-scale problems, our approach produces decompositions that outperform those produced by state-of-the-art partitioners like METIS and even those that are manually constructed by domain experts. Copyright © 2017 John Wiley & Sons, Ltd.

A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared with other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared with existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton–Raphson method and comparable speed and robustness to a line search augmented scheme. Copyright © 2017 John Wiley & Sons, Ltd.

The morphology of many naturally occurring and man-made materials at different length scales can be modelled using the packing of correspondingly shaped and sized particles. The mechanical behaviour of this vast category of materials – which includes granular media, particle reinforced materials and foams - depends strongly upon the shape and size distribution of the particles. This paper presents a method for the generation and packing of arbitrarily shaped polyhedral particles. The algorithm for the generation of the particles is based on the Voronoi tessellation technique, whilst the packing is performed using a geometrical approach, which guarantees the non-overlapping of the bodies without relying upon any, otherwise typically computationally expensive, contact detection and interaction algorithm. The introduction of three geometrical parameters allows to control the shape, size and spacial density of the polyhedral particles, which are used to build numerical models representative of densely packed granular assemblies, granular reinforced materials and closed-cell foams. Copyright © 2017 John Wiley & Sons, Ltd.

This paper presents a comprehensive study on the use of Irwin's crack closure integral for direct evaluation of mixed-mode stress intensity factors (SIFs) in curved crack problems, within the extended finite element method. The approach employs high-order enrichment functions derived from the standard Williams asymptotic solution, and SIFs are computed in closed form without any special post-processing requirements. Linear triangular elements are used to discretize the domain, and the crack curvature within an element is represented explicitly. An improved quadrature scheme using high-order isoparametric mapping together with a generalized Duffy transformation is proposed to integrate singular fields in tip elements with curved cracks. Furthermore, because the Williams asymptotic solution is derived for straight cracks, an appropriate definition of the angle in the enrichment functions is presented and discussed. This contribution is an important extension of our previous work on straight cracks and illustrates the applicability of the SIF extraction method to curved cracks.

The performance of the method is studied on several circular and parabolic arc crack benchmark examples. With two layers of elements enriched in the vicinity of the crack tip, striking accuracy, even on relatively coarse meshes, is obtained, and the method converges to the reference SIFs for the circular arc crack problem with mesh refinement. Furthermore, while the popular interaction integral (a variant of the J-integral method) requires special auxiliary fields for curved cracks and also needs cracks to be sufficiently apart from each other in multicracks systems, the proposed approach shows none of those limitations. Copyright © 2017 John Wiley & Sons, Ltd.

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. To examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space of the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model. Copyright © 2016 John Wiley & Sons, Ltd.

The LATIN (acronym of LArge Time INcrement) method was originally devised as a non-incremental procedure for the solution of quasi-static problems in continuum mechanics with material nonlinearity. In contrast to standard incremental methods like Newton and modified Newton, LATIN is an iterative procedure applied to the entire loading path. In each LATIN iteration, two problems are solved: a local problem, which is nonlinear but algebraic and miniature, and a global problem, which involves the entire loading process but is linear. The convergence of these iterations, which has been shown to occur for a large class of nonlinear problems, provides an approximate solution to the original problem. In this paper, the LATIN method is presented from a different viewpoint, taking advantage of the causality principle. In this new view, LATIN is an incremental method, and the LATIN iterations are performed within each load step, similarly to the way that Newton iterations are performed. The advantages of the new approach are discussed. In addition, LATIN is extended for the solution of time-dependent wave problems. As a relatively simple model for illustrating the new formulation, lateral wave propagation in a flat membrane made of a nonlinear material is considered. Numerical examples demonstrate the performance of the scheme, in conjunction with finite element discretization in space and the Newmark trapezoidal algorithm in time. Copyright © 2017 John Wiley & Sons, Ltd.

This paper presents a novel formulation based on Hellinger–Reissner variational principle in the framework of quasi-conforming method for static and free vibration analysis of Reissner–Mindlin plates. The formulation starts from polynomial approximation of stresses, which satisfy the equilibrium equations of Reissner–Mindlin plate theory. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the string-net functions are introduced to calculate strain integration. As examples, two new plate bending elements, a 4-node quadrilateral element QC-P4-11*β* and a 3-node triangular element QC-P3-7*β*, are proposed. Several benchmark examples are demonstrated to show the performance of the elements, and the results obtained are compared with other available ones. Numerical results have proved that both elements possess excellent precision. In particular, the quadrilateral element performs well even when the element shape degenerates into a triangle or concave quadrangle. Copyright © 2017 John Wiley & Sons, Ltd.

The hyper-reduced-order model (HROM) is proposed for the thermal calculation with a constant moving thermal load. Firstly, the constant velocity transient process is simplified to a steady-state process in the moving frame. Secondly, the control volume is determined by the temperature rate, and the thermal equilibrium equation in the moving frame is derived by introducing an advective term containing the loading velocity. Thirdly, the HROM is performed on the control volume with a moving frame formulation. This HROM has been applied to the thermal loading on brick and ring disk specimens with a CPU gain of the order of 7 (10^{7}). In addition, two strategies are proposed for the HROM to improve its precision. Moreover, the high efficiency and high accuracy are kept for the parametric studies on thermal conductivity and amplitude of heat flux based on the developed HROM. Copyright © 2016 John Wiley & Sons, Ltd.

This work provides a robust variational-based numerical implementation of a phase field model of ductile fracture in elastic–plastic solids undergoing large strains. This covers a computationally efficient *micromorphic regularization* of the coupled gradient plasticity-damage formulation. The phase field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with geometric features rooted in fracture mechanics. It has proven immensely successful with regard to the analysis of complex crack topologies without the need for fracture-specific computational structures such as finite element design of crack discontinuities or intricate crack-tracking algorithms. The proposed gradient-extended plasticity-damage formulation includes two independent length scales that regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones or vice versa and guarantees on the computational side a mesh objectivity in post-critical ranges. The proposed setting is rooted in a canonical variational principle. The coupling of gradient plasticity to gradient damage is realized by a constitutive work density function that includes the stored elastic energy and the dissipated work due to plasticity and fracture. The latter represents a coupled resistance to plasticity and damage, depending on the gradient-extended internal variables that enter plastic yield functions and fracture threshold functions. With this viewpoint on the generalized internal variables at hand, the thermodynamic formulation is outlined for gradient-extended dissipative solids with generalized internal variables that are passive in nature. It is specified for a conceptual model of von Mises-type elasto-plasticity at finite strains coupled with fracture. The canonical theory proposed is shown to be governed by a rate-type minimization principle, which fully determines the coupled multi-field evolution problem. This is exploited on the numerical side by a fully symmetric monolithic finite element implementation. An important aspect of this work is the regularization towards a micromorphic gradient plasticity-damage setting by taking into account additional internal variable fields linked to the original ones by penalty terms. This enhances the robustness of the finite element implementation, in particular, on the side of gradient plasticity. The performance of the formulation is demonstrated by means of some representative examples. Copyright © 2016 John Wiley & Sons, Ltd.

The most used method for calculation of mechanical properties of the fibre-reinforced composites on the scale of unit cell of the reinforcement consists in continuous meshing of the reinforcement and matrix volumes. Often, this leads to bad quality or large size of the generated mesh. Mesh superposition (MSP) techniques allow overcoming these issues by independent meshing of both components while coupling them together based on constraint equations. In the present work, two different implementations of MSP techniques are investigated in detail, and results are compared with a common method and experiment for a simple unidirectional reinforcement geometry and a complex 3D weave composite. An MSP formulation for large deformations case is described. Results show good agreement in local strain distributions and in prediction of the homogenized mechanical properties. Copyright © 2016 John Wiley & Sons, Ltd.

The study of molecular flows at low Knudsen numbers (∼0.1–0.5), over nano-scaled objects of 20–100 nm size is becoming an important area of research. The simulation of fluid–structure interaction at nano-scale is important for understanding the adsorption and drag resistance characteristics of nano-devices in the fields of drug delivery, surface cleaning and protein movement.

A novel formulation has been proposed that calculates localised values for both the kinetic and configurational parts of the Irving–Kirkwood stress tensor at given fixed positions within the computational domain.

Macroscopic properties, such as streaming velocity, pressure and drag coefficients, are predicted by modelling the fluid–structure interaction using a moving least-squares method. The gravitation-driven molecular flow is examined over three different cross-sectional shapes—i.e. diamond-, circular- and square-shaped cylinders—confined within parallel walls and has been simulated for rough and smooth surfaces.

The molecular dynamics formulation has allowed, for the first time, the calculation of localised drag forces over nano-cylinders. The computational simulation has shown that existing methods, including continuum-based approaches, significantly underestimate drag coefficients over nano-cylinders. The proposed molecular dynamics formulation has been verified on simulation based tests, as experimental and analytical results are unavailable at this scale. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a numerical investigation of microscopic lubricant flows from the cavities to the plateaus of the surface roughness of metal sheets during forming processes. This phenomenon, called micro-plasto-hydrodynamic lubrication, was observed experimentally in various situations such as compression sliding tests, strip drawing and cold rolling. It leads to local friction drop and wear reduction. It is therefore critical to achieve a good understanding of this phenomenon. As to move towards that goal, a multiscale fluid–structure interaction model is developed to model lubricant flows at the microscopic scale. These simulations are made possible through the use of the Arbitrary Lagrangian Eulerian (ALE) formalism. In this paper, this methodology is used to study plane strip drawing. The numerical model is able to predict the onset of lubricant escape and the amount of lubricant flowing on the plateaus. Numerical results exhibit good agreement with experimental measurements. Copyright © 2017 John Wiley & Sons, Ltd.

We consider model reduction for magneto-quasistatic field equations in the vector potential formulation. A finite element discretization of such equations leads to large-scale differential-algebraic equations of special structure. For model reduction of linear systems, we employ a balanced truncation approach, whereas nonlinear systems are reduced using a proper orthogonal decomposition method combined with a discrete empirical interpolation technique. We will exploit the special block structure of the underlying problem to improve the performance of the model reduction algorithms. Furthermore, we discuss an efficient evaluation of the Jacobi matrix required in nonlinear time integration of the reduced models. Copyright © 2017 John Wiley & Sons, Ltd.

Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for example. The objective function is commonly expressed in terms of moments of these quantities, such as the mean, standard deviation, or even higher-order moments. Polynomial surrogate models based on polynomial chaos expansions have often been implemented in this respect. The original approach of uncertainty quantification using polynomial chaos is however intrusive. It is based on a Galerkin-type formulation of the model equations to derive the governing equations for the polynomial expansion coefficients. Third-order, indeed fourth-order moments of the polynomials are needed in this analysis. Besides, both intrusive and non-intrusive approaches call for their computation provided that higher-order moments of the quantities of interest need to be post-processed. In most applications, they are evaluated by Gauss quadratures and eventually stored for use throughout the computations. In this paper, analytical formulas are rather considered for the moments of the continuous polynomials of the Askey scheme, so that they can be evaluated by quadrature-free procedures instead. Matlab^{©} codes have been developed for this purpose and tested by comparisons with Gauss quadratures. Copyright © 2017 John Wiley & Sons, Ltd.

This work deals with the formulation and implementation of a mixed finite element formulation for nonlinear thermoelasticity. In the literature, a ‘consistent’ mixed formulation to reduce spurious oscillations in thermal stresses has been developed which involves the use of a temperature interpolation that is one order lower than the displacement interpolation functions. However, such a strategy would require a very fine mesh in problems where thermal gradients are high. In order to reduce the computational cost, we propose a new hybrid formulation for both the mechanical and thermal parts of the stress tensor, that not only overcomes membrane, shear, and volumetric locking but also eliminates thermal stress oscillations, even with the use of a coarse mesh. For transient problems, a new energy-momentum conserving time stepping scheme is also proposed so that linear and angular momenta and energy are conserved exactly in the fully discrete hybrid framework in the absence of loading and dissipation. Several examples for the St. Venant–Kirchhoff and Ogden material models where the solutions are compared against either analytical or other numerical strategies show the efficacy of the developed procedure. Copyright © 2016 John Wiley & Sons, Ltd.

Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate conservation of numerical fluxes. This numerical flux conservation is performed within the usual moving least squares framework. Unlike Finite Volume Methods, it is based on locally defined control cells, rather than a globally defined mesh. We present the application of this method to an advection diffusion equation and the incompressible Navier–Stokes equations. Our simulations show that the introduction of flux conservation significantly reduces the errors in conservation in meshfree GFDMs. Copyright © 2017 John Wiley & Sons, Ltd.

A new approach based on the use of the Newton and level set methods allows to follow the motion of interfaces with surface tension immersed in an incompressible Newtonian fluid. Our method features the use of a high-order fully implicit time integration scheme that circumvents the stability issues related to the explicit discretization of the capillary force when capillary effects dominate. A strategy based on a consistent Newton–Raphson linearization is introduced, and performances are enhanced by using an exact Newton variant that guarantees a third-order convergence behavior without requiring second-order derivatives. The problem is approximated by mixed finite elements, while the anisotropic adaptive mesh refinements enable us to increase the computational accuracy. Numerical investigations of the convergence properties and comparisons with benchmark results provide evidence regarding the efficacy of the methodology. The robustness of the method is tested with respect to the standard explicit method, and stability is maintained for significantly larger time steps compared with those allowed by the stability condition. Copyright © 2016 John Wiley & Sons, Ltd.

When computing the homogenized response of a representative volume element (RVE), a popular choice is to impose periodic boundary conditions on the RVE. Despite their popularity, it is well known that standard periodic boundary conditions lead to inaccurate results if cracks or localization bands in the RVE are not aligned with the periodicity directions. A previously proposed remedy is to use modified strong periodic boundary conditions that are aligned with the dominating localization direction in the RVE. In the present work, we show that alignment of periodic boundary conditions can also conveniently be performed on weak form. Starting from a previously proposed format for weak micro-periodicity that does not require a periodic mesh, we show that aligned weakly periodic boundary conditions may be constructed by only modifying the mapping (mirror function) between the associated parts of the RVE boundary. In particular, we propose a modified mirror function that allows alignment with an identified localization direction. This modified mirror function corresponds to a shifted stacking of RVEs, and thereby ensures compatibility of the dominating discontinuity over the RVE boundaries. The proposed method leads to more accurate results compared to using unaligned periodic boundary conditions, as demonstrated by the numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

The optimal design of mechanical structures subject to periodic excitations within a large frequency interval is quite challenging. In order to avoid bad performances for non-discretized frequencies, it is necessary to finely discretize the frequency interval, leading to a very large number of state equations. Then, if a standard adjoint-based approach is used for optimization, the computational cost (both in terms of CPU and memory storage) may be prohibitive for large problems, especially in three space dimensions. The goal of the present work is to introduce two new non-adjoint approaches for dealing with frequency response problems in shape and topology optimization. In both cases, we rely on a classical modal basis approach to compute the states, solutions of the direct problems. In the first method, we do not use any adjoint but rather directly compute the shape derivatives of the eigenmodes in the modal basis. In the second method, we compute the adjoints of the standard approach by using again the modal basis. The numerical cost of these two new strategies are much smaller than the usual ones if the number of modes in the modal basis is much smaller than the number of discretized excitation frequencies. We present numerical examples for the minimization of the dynamic compliance in two and three space dimensions. Copyright © 2017 John Wiley & Sons, Ltd.

A computationally efficient numerical model that describes carbon sequestration in deep saline aquifers is presented. The model is based on the multiphase flow and vertically averaged mass balance equations, requiring the solution of two partial differential equations – a pressure equation and a saturation equation. The saturation equation is a nonlinear advective equation for which the application of Galerkin finite element method (FEM) can lead to non-physical oscillations in the solution. In this article, we extend three stabilized FEM formulations, which were developed for uncoupled systems, to the governing nonlinear coupled PDEs. The methods developed are based on the streamline upwind, the streamline upwind/Petrov–Galerkin and the least squares FEM. Two sequential solution schemes are developed: a single step and a predictor–corrector. The range of Courant numbers yielding smooth and oscillation-free solutions is investigated for each method. The useful range of Courant numbers found depends upon both the sequential scheme (single step vs predictor–corrector) and also the time integration method used (forward Euler, backward Euler or Crank–Nicolson). For complex problems such as when two plumes meet, only the SU stabilization with an amplified stabilization parameter gives satisfactory results when large time steps are used. Copyright © 2016 John Wiley & Sons, Ltd.

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

Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non-uniqueness. Copyright © 2016 The Authors. *International Journal for Numerical Methods in Engineering* Published by John Wiley & Sons Ltd.

This work investigates the use of hierarchical mesh decomposition strategies for topology optimisation using bi-directional evolutionary structural optimisation algorithm. The proposed method uses a dual mesh system that decouples the design variables from the finite element analysis mesh. The investigation focuses on previously unexplored areas of these techniques to investigate the effect of five meshing parameters on the analysis solving time (i.e. computational effort) and the analysis quality (i.e. solution optimality). The foreground mesh parameters, including adjacency ratio and minimum and maximum element size, were varied independently across solid and void domain regions. Within the topology optimisation, strategies for controlling the mesh parameters were investigated. The differing effects of these parameters on the efficiency and efficacy of the analysis and optimisation stages are discussed, and recommendations are made for parameter combinations. Some of the key findings were that increasing the adjacency ratio increased the efficiency only modestly – the largest effect was for the minimum and maximum element size parameters – and that the most dramatic reduction in solve time can be achieved by not setting the minimum element size too low, assuming mapping onto a background mesh with a minimum element size of 1. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd.

This paper focuses on a new framework for obtaining a nonintrusive (i.e., not requiring projecting of the governing equations onto the reduced basis modes) reduced order model for two-dimensional fluid problems. To overcome the shortcomings of intrusive model order reduction usually derived by combining the Proper Orthogonal Decomposition and the Galerkin projection methods, we developed a novel technique on the basis of randomized dynamic mode decomposition (DMD) as a fast and accurate option in model order reduction. Our approach utilizes an adaptive randomized DMD to obtain a reduced basis in the offline stage, and then the temporal values of the reduced order model are obtained in the online stage through an interpolation using radial basis functions. The rank of the reduced DMD model is given as the unique solution of a constrained optimization problem. The Saint-Venant (shallow water) equations in a channel on the rotating earth are employed to provide the numerical data. We emphasize the excellent behavior of the nonintrusive reduced order model by performing a qualitative analysis. In addition, we gain a significantly reduction of CPU time in computation of the reduced order models compared with the classical DMD method. Copyright © 2016 John Wiley & Sons, Ltd.

In this contribution, a three-dimensional frictional contact formulation in the form of an interface solid finite element is discussed. The interface element incorporates normal as well as tangential contact conditions and aims at the modeling of phenomena occurring in engineering problems on the interface between different materials. The focus of this work lies on the description of the tangential interaction of bodies on their contact interface. Instead of the widely used Coulomb friction law, a simple elastoplastic material law is applied in order to model the interaction mechanism on the tangent plane. Appropriate local coordinate systems are introduced on the surface and point of contact, and all contact operations are performed in these coordinate systems by adopting a fully covariant description. In this way, we derive a symmetric element stiffness matrix not only for the case of sticking but also for sliding. Exploiting the advantages of the covariant description, we show that the fact that the derived stiffness matrix discretely consists of constitutive and geometrical parts enables us to introduce rather straightforwardly new appropriate interface laws describing the tangential interaction of the contacting bodies. The presented numerical results show very good correlation of the developed approach with ‘pull-out’ experiments. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we present an effective 6-node triangular solid-shell element (MITC-S6), with particular attention on shear locking and thickness locking. To alleviate shear locking, the assumed transverse strain field of the MITC3+ shell element is used while modifying the bending enhancement mechanism. Thickness locking is treated using the assumed and enhanced strain methods for thickness strain. Two independent enhancements of strains are applied: The in-plane and transverse shear strain fields are enhanced using the strain fields obtained from a bubble interpolation function for in-plane translations, and the thickness strain field is enhanced for linear variation in the thickness direction. The general three-dimensional material law is employed. The proposed element passes all the basic tests including zero-energy mode, patch, and isotropy tests. Excellent performance is observed in various linear and nonlinear benchmark tests, wherein its performance is compared with that of existing 6-node triangular and 8-node quadrilateral solid-shell elements. Copyright © 2016 John Wiley & Sons, Ltd.

As a typical high-dimensional nonlinear dynamic problem, the difficulties of the dynamic analysis on the spatial flexible damping beam mostly result from the coupling between the spatial motion and the transverse vibration. Considering the coupling effect and the weak structure damping, the dynamic behaviors of the spatial flexible beam are investigated by a complex structure-preserving method in this paper. Based on the variational principle, the dynamic model of the spatial flexible damping beam is established, which can be decoupled into two parts approximately, one controls the spatial motion and another mainly controls the transverse vibration. For the first part, the classic fourth-order Runge–Kutta method can be used to discrete it expediently. For the latter part, based on the generalized multi-symplectic idea, the approximate symmetric form as well as the generalized multi-symplectic conservation law is formulated, and a 15-point scheme equivalent to the Preissmann scheme is constructed. Numerical iterations are performed for six typical initial cases between the two parts to study the dynamic behaviors of the spatial flexible beam. In the numerical experiments, the effects of the damping factor and the initial conditions (including the initial radial velocity and the initial attitude angle) on the dynamic behaviors of the spatial flexible beam are investigated in detail. From the numerical results, it can be concluded that the damping effect on the long-time dynamic behaviors of the spatial flexible beam could not be neglected even if it is weak; the numerical method proposed in this paper owns the tiny numerical dissipation as well as the excellent long-time numerical stability. Copyright © 2016 John Wiley & Sons, Ltd.

An accurate spectral-sampling surface method for the vibration analysis of 2-D curved beams with variable curvatures and general boundary conditions is presented. The method combines the advantages of the sampling surface method and spectral method. The formulation is based on the 2-D elasticity theory, which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced. Specifically, a set of non-equally spaced sampling surfaces parallel to the beam's middle surface are primarily collocated along the thickness direction, and the displacements of these surfaces are chosen as fundamental beam unknowns. This fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces. Each of the fundamental beam unknowns is then invariantly expanded as Chebyshev polynomials of the first kind, and the problems are stated in variational form with the aid of the penalty technique and Lagrange multipliers, which provide complete flexibility to describe any arbitrary boundary conditions. Finally, the desired solutions are obtained by the variational operation. Copyright © 2016 John Wiley & Sons, Ltd.

This paper details a semi-analytical procedure to efficiently integrate the product of a smooth function and a complex exponential over tetrahedral elements. These highly oscillatory integrals appear at the core of different numerical techniques. Here, the partition of unity method enriched with plane waves is used as motivation. The high computational cost or the lack of accuracy in computing these integrals is a bottleneck for their application to engineering problems of industrial interest. In this integration rule, the non-oscillatory function is expanded into a set of Lagrange polynomials. In addition, Lagrange polynomials are expressed as a linear combination of the appropriate set of monomials, whose product with the complex exponentials is analytically integrated, leading to 16 specific cases that are developed in detail. Finally, we present several numerical examples to assess the accuracy and the computational efficiency of the proposed method, compared with standard Gauss–Legendre quadratures. Copyright © 2016 John Wiley & Sons, Ltd.

The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially around the eigenfrequencies of the dynamical system. In the present study, a new approach based on Padé approximants to obtain moments and pdf of the dynamic response in the frequency domain is proposed. A key difference between the direct polynomial chaos representation and the Padé representation is that the Padé approach has polynomials in both numerator and denominator. For frequency response functions, the denominator plays a vital role as it contains the information related to resonance frequencies, which are uncertain. A Galerkin approach in conjunction with polynomial chaos is proposed for the Padé approximation. Another physics-based approach, utilizing polynomial chaos expansions of the random eigenmodes, is proposed and compared with the proposed Padé approach. It is shown that both methods give accurate results even if a very low degree of the polynomial expansion is used. The methods are demonstrated for two degree-of-freedom system with one and two uncertain parameters. Copyright © 2016 John Wiley & Sons, Ltd.

We propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms. Copyright © 2016 John Wiley & Sons, Ltd.

The parametric analysis of electric grids requires carrying out a large number of power flow computations. The different parameters describe loading conditions and grid properties. In this framework, the proper generalized decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to (1) iterating algebraic solver, (2) number of terms in the separable greedy expansion, and (3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end-user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the quantity of interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems. Copyright © 2016 John Wiley & Sons, Ltd.

The paper presents the generalization of the modification of classical boundary integral equation and obtaining parametric integral equation system for 2D elastoplastic problems. The modification was made to obtain such equations for which numerical solving does not require application of finite or boundary elements. This was achieved through the use of curves and surfaces for modeling introduced at the stage of analytical modification of the classic boundary integral equation. For approximation of plastic strains the Lagrange polynomials with various number and arrangement of interpolation nodes were used. Reliability of the modification was verified on examples with analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a level set-based shape and topology optimization method for conceptual design of cast parts. In order to be successfully manufactured by the casting process, the geometry of cast parts should satisfy certain moldability conditions, which poses additional constraints in the shape and topology optimization of cast parts. Instead of using the originally point-wise constraint statement, we propose a casting constraint in the form of domain integration over a narrowband near the material boundaries. This constraint is expressed in terms of the gradient of the level set function defining the structural shape and topology. Its explicit and analytical form facilitates the sensitivity analysis and numerical implementation. As compared with the standard implementation of the level set method based on the steepest descent algorithm, the proposed method uses velocity field design variables and combines the level set method with the gradient-based mathematical programming algorithm on the basis of the derived sensitivity scheme of the objective function and the constraints. This approach is able to simultaneously account for the casting constraint and the conventional material volume constraint in a convenient way. In this method, the optimization process can be started from an arbitrary initial design, without the need for an initial design satisfying the cast constraint. Numerical examples in both 2D and 3D design domain are given to demonstrate the validity and effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we propose a numerical method based on an active structural control to dampen the discrete critical frequencies from a fe/be coupled system, which models a time-harmonic fluid-structure interaction problem. The active structural acoustic control used consists of applying external forces directly on the structure, so that in the presence of critical frequencies, the linear system remains stable and, in turn, in the presence of non-critical frequencies, the active control does not alter the system. We consider the problem in the framework of the theory of optimal control and present bi-dimensional numerical simulations to show the behavior of the scheme in some vibro-acoustic structures. Copyright © 2016 John Wiley & Sons, Ltd.

An upscaling approach for multi-porosity media is developed and demonstrated on a three-scale porous medium. The three-scale porous medium problem is analyzed using the so-called MultiSPH approach, which is a sequential smooth particle hydrodynamics (SPH) solver at multiple scales. By this approach, upscaling introduces drag forces on the SPH particles at coarser scales. The resulting permeabilities obtained by the MultiSPH approach are validated against available analytical solutions for simple microstructures. For complex microstructures, the MultiSPH approach is validated against detailed single-scale SPH simulations and experimental data. Sensitivities of fluid–structure interaction on the permeability is investigated. Copyright © 2016 John Wiley & Sons, Ltd.

This paper develops an enhanced response sensitivity approach for structural damage identification. The whole work is mainly two-fold. Firstly, the general response sensitivity approach has been shown to perform well for small damage, but may not work for moderate or large damage. Therefore, to overcome this drawback, the trust-region restriction is additionally enforced to enhance the general response sensitivity approach. In doing so, the Tikhonov regularization is invoked which is simple for practical manipulation and is shown equivalent to trust-region considerations. Secondly, concrete convergence analysis is presented to guarantee the performance of the enhanced response sensitivity approach. Numerical examples are studied to verify the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

This study presents a gradient-based shape optimization over a fixed mesh using a non-uniform rational B-splines-based interface-enriched generalized finite element method, applicable to multi-material structures. In the proposed method, non-uniform rational B-splines are used to parameterize the design geometry precisely and compactly by a small number of design variables. An analytical shape sensitivity analysis is developed to compute derivatives of the objective and constraint functions with respect to the design variables. Subtle but important new terms involve the sensitivity of shape functions and their spatial derivatives. Verification and illustrative problems are solved to demonstrate the precision and capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.

A mean-strain 10-node tetrahedral element is developed for the solution of geometrically nonlinear solid mechanics problems using the concept of energy-sampling stabilization. A uniform-strain tetrahedron for applications to linear elasticity was recently described. The formulation as extended here is able to solve large-strain hyperelasticity. The present 10-node tetrahedron is composed of several four-node linear tetrahedral elements, four tetrahedra in the corners, and four tetrahedra that tile the central octahedron in three possible sets of four-node tetrahedra, corresponding to three different choices for the internal diagonal. We formulate a mean-strain element with stabilization energy evaluated on the four corner tetrahedra, which is shown to guarantee consistency and stability. The stabilization energy is expressed through a stored-energy function, and contact with input parameters in the small-strain regime is made. The neo-Hookean model is used to formulate the stabilization energy. As for small-strain elasticity, the stabilization parameters are determined by actual material properties and geometry of a tetrahedra without any user input. The numerical tests demonstrate that the present element performs well for solid, shell, and nearly incompressible structures. Copyright © 2016 John Wiley & Sons, Ltd.

For the two-dimensional three-temperature radiative heat conduction problem appearing in the inertial confinement numerical stimulations, we choose the *Freezing coefficient method* to linearize the nonlinear equations, and initially apply the well-known mixed finite element scheme with the lowest order Raviart–Thomas element associated with the triangulation to the linearized equations, and obtain the convergence with one order with respect to the space direction for the temperature and flux function approximations, and design a simple but efficient algorithm for the discrete system. Three numerical examples are displayed. The former two verify theoretical results and show the super-convergence for temperature and flux functions at the barycenter of the element, which is helpful for solving the radiative heat conduction problems. The third validates the robustness of this scheme with small energy conservative error and one order convergence for the time discretization. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, we propose a homogenization formulation to model transient heat conduction in heterogeneous media that takes into account thermal inertia contributions, which arise from a finite description of the microscale. Rewriting the variational form of the transient heat conduction problem and making use of key assumptions, we arrive at a mathematical formulation that suggests an extension of the Hill–Mandel principle when considering non-null heat flux divergence in the representative volume element (RVE). Along the manuscript, we highlight that the main results of the proposed formulation are in agreement with recent advances in the field of computational homogenization applied to transient mechanical and heat flow problems. The proposed extension of the Hill–Mandel principle contributes to the understanding of the microscale thermal inertia effects incorporation into the multiscale framework. We also present the calculations needed for implementing the model and numerical results, which give support to the theoretical model developed. The numerical results highlight the importance of considering full transient aspects when dealing with multiscale heat conduction in heterogeneous media which are subjected to high thermal gradients. Copyright © 2016 John Wiley & Sons, Ltd.

For the response analysis of engineering systems with uncertain-but-bounded parameters, three uncertain models have been considered according to the available probability distribution information. One is the bounded random model in which the uncertain parameters are well defined with sufficient probability distribution information and described as bounded random variables. The second one is the interval model in which the uncertain parameters are expressed as interval variables without giving any information of probability distribution. The last one is the bounded hybrid uncertain model, which includes both bounded random variables and interval variables. On the basis of Gegenbauer polynomial approximation theory, a unified *interval and random Gegenbauer series expansion* (IRGSE) method is proposed and extended for the response prediction of three uncertain models of acoustic fields with uncertain-but-bounded parameters. In IRGSE, the uncertain-but-bounded variables with different probability distribution information, including interval variables and bounded random variables with different *probability density functions*, are transformed into the function of unitary variables defined on [-1,1] associated with the corresponding polynomial parameter (*λ*) of *Gegenbauer series expansion* (GSE). The coefficients of GSE is calculated by Gauss–Gegenbauer integration method. By using IRGSE, the responses of three uncertain acoustic models are approximated uniformly by GSE, through which the interval and random analysis can be easily implemented by many numerical solvers. Two numerical examples are applied to investigate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

This work investigates a model reduction method applied to coupled multi-physics systems. The case in which a system of interest interacts with an external system is considered. An approximation of the Poincaré–Steklov operator is computed by simulating, in an offline phase, the external problem when the inputs are the Laplace–Beltrami eigenfunctions defined at the interface. In the online phase, only the reduced representation of the operator is needed to account for the influence of the external problem on the main system. An online basis enrichment is proposed in order to guarantee a precise reduced-order computation. Several test cases are proposed on different fluid–structure couplings. Copyright © 2016 John Wiley & Sons, Ltd.

The singular boundary method (SBM) is a recent strong-form boundary collocation method that uses a linear combination of the fundamental solution of the governing equation to approximate the field variables. Because of its full interpolation matrix, the SBM solution encounters the high computational complexity and storage requirement that limit its applications to large-scale engineering problems. This paper presents a way to overcome this drawback by introducing the diagonal form fast multipole method. A diagonal form fast multipole singular boundary method is then developed to reduce the computational operations of the SBM with direct solvers from *O*(*N*^{3}) to *O*(*N*log*N*), where *N* is the number of unknowns. The proposed method works well for acoustic radiation and scattering with nondimensional wave number *kD*<110 (*k* is the wave number and *D* the maximum diameter of the computational domain). Several numerical experiments are provided to show the efficiency and accuracy of the present strategy, including the radiation from a nuclear submarine and the scattering from an airplane. The numerical results clearly demonstrate that the present diagonal form fast multipole singular boundary method breaks the limitations of the SBM and successfully simulates the large-scale acoustic problems with more than one million unknowns on a desktop computer. Copyright © 2016 John Wiley & Sons, Ltd.

Response sensitivity is an essential component to understanding the complexity of material and geometric nonlinear finite element formulations of structural response. The direct differentiation method (DDM), a versatile approach to computing response sensitivity, requires differentiation of the equations that govern the state determination of an element and it produces accurate and efficient results. The DDM is applied to a force-based element formulation that utilizes curvature-shear-based displacement interpolation (CSBDI) in its state determination for material and geometric nonlinearity in the basic system of the element. The response sensitivity equations are verified against finite difference computations, and a detailed example shows the effect of parameters that control flexure–shear interaction for a stress resultant plasticity model. The developed equations make the CSBDI force-based element available for gradient-based applications such as reliability and optimization where efficient computation of response sensitivities is necessary for convergence of gradient-based search algorithms. Copyright © 2016 John Wiley & Sons, Ltd.

In the present paper, strong form finite elements are employed for the free vibration study of laminated arbitrarily shaped plates. In particular, the stability and accuracy of three different Fourier expansion-based differential quadrature techniques are shown. These techniques are used to solve the partial differential system of equations inside each computational element. The three approaches are called harmonic differential quadrature, Fourier differential quadrature and improved Fourier expansion-based differential quadrature methods. The improved Fourier expansion-based differential quadrature method implements auxiliary functions in order to approximate functional derivatives up to the fourth order, with respect to the Fourier differential quadrature method that has a basis made of sines and cosines. All the present applications are related to literature comparisons and the presentation of new results for further investigation within the same topic. A study of such kind has never been proposed in the literature, and it could be useful as a reference for future investigation in this matter. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely, we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), and (3) a procedure to build admissible fields for dual-primal finite element tearing and interconnecting and balancing domain decomposition by constraints methods leading to an error bound that separates the contributions of the solver and of the discretization. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a discontinuous thick level set model for modeling delamination initiation and propagation in composites. Interface elements are widely applied in delamination models to define a discontinuity between layers of a laminate. In this paper, the common damage definition in the constitutive relation of interface elements is replaced with a new definition developed using the thick level set approach. Following this approach, a band of damage with predefined length is considered where the damage is defined as a function of distance to the damage front. The specifications of suitable damage functions for the developed method are investigated, and an efficient damage function is introduced. A sensitivity analysis of numerical input parameters is performed, which proves that the model is not sensitive to the length of the damage band. Because the required element size is linked to the length of the damage band, the insensitivity to this length provides freedom to use coarser meshes. Furthermore, the model provides a direct link between fracture mechanics and damage mechanics, which enables further development of the model for fatigue analysis. Validation of this model is presented by conducting three-dimensional mode I, mode II, and mixed-mode simulations and comparing the results with analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.

The present work introduces an efficient technique for the deformation of block-structured grids occurring in simulations of fluid–structure interaction (FSI) problems relying on large-eddy simulation (LES). The proposed hybrid approach combines the advantages of the inverse distance weighting (IDW) interpolation with the simplicity and low computational effort of transfinite interpolation (TFI), while preserving the mesh quality in boundary layers. It is an improvement over the state-of-the-art currently in use. To reach this objective, in a first step, three elementary mesh deformation methods (TFI, IDW, and radial basis functions) are investigated based on several test cases of different complexities analyzing not only their capabilities but also their computational costs. That not only allows to point out the advantages of each method but also demonstrates their drawbacks. Based on these specific properties of the different methods, a hybrid methodology is suggested that splits the entire grid deformation into two steps: first, the movement of the block-boundaries of the block-structured grid and second, the deformation of each block of the grid. Both steps rely on different methodologies, which allows to work out the most appropriate method for each step leading to a reasonable compromise between the grid quality achieved and the computational effort required. Finally, a hybrid IDW-TFI methodology is suggested that best fits to the specific requirements of coupled FSI-LES applications. This hybrid procedure is then applied to a real-life FSI-LES case. Copyright © 2016 John Wiley & Sons, Ltd.

We present an approach for controlling the undercut and the minimal overhang angle in density based topology optimization, which are useful for reducing support structures in additive manufacturing. We cast both the undercut control and the minimal overhang angle control that are inherently constraints on the boundary shape into a domain integral of Heaviside projected density gradient. Such a Heaviside projection based integral of density gradient leads to a single constraint for controlling the undercut or controlling the overhang angle in the optimization. It effectively corresponds to a constraint on the projected perimeter that has undercut or has slope smaller than the prescribed overhang angle. In order to prevent trivial solutions of intermediate density to satisfy the density gradient constraints, a constraint on density grayness is also incorporated into the formulations. Numerical results on Messerschmitt–Bolkow–Blohm beams, cantilever beams, and 2D and 3D heat conduction problems demonstrate the proposed formulations are effective in controlling the undercut and the minimal overhang angle in the optimized designs. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient algorithms are considered for the computation of a reduced-order model based on the proper orthogonal decomposition methodology for the solution of parameterized elliptic partial differential equations. The method relies on partitioning the parameter space into subdomains based on the properties of the solution space and then forming a reduced basis for each of the subdomains. This yields more efficient offline and online stages for the proper orthogonal decomposition method. We extend these ideas for inexpensive adjoint based a posteriori error estimation of both the expensive finite element method solutions and the reduced-order model solutions, for a single and multiple quantities of interest. Various numerical results indicate the efficacy of the approach. Copyright © 2016 John Wiley & Sons, Ltd.

The representation of structural boundaries is of significant importance for the applications of the discrete element method in an industry. In recent decades, triangle meshes are extensively used for representing structural boundaries. Structural boundaries of industrial objects are composed by regular shapes and irregular shapes in many occasions. A method for representing structural boundaries with regular shapes and irregular shapes has been developed by combining mathematical equations and triangle meshes for computational efficiency. When structural boundaries are represented by mathematical equations and triangle meshes, gaps or protuberances may exist at the connection boundaries between regular shapes and irregular shapes. For the exactness of representation of structural boundaries, gaps or protuberances are identified, expressed and treated successively, so that the geometrical shapes composed by regular shapes described with mathematical equations and irregular shapes described with triangle meshes can replace the original structural shapes. Two series of numerical tests have been conducted to verify this method. The results showed that this method can effectively represent complicated structural boundaries containing regular shapes and irregular shapes and greatly reduce computational cost in the contact detection between particles and structural boundaries. Copyright © 2016 John Wiley & Sons, Ltd.

The quasicontinuum (QC) method is a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. While traditional QC methods thereby create interfaces between fully resolved and coarse-grained regions, the recently introduced fully nonlocal QC framework does not fundamentally differentiate between atomistic and coarsened domains. Adding adaptive refinement enables us to tie atomistic resolution to evolving regions of interest such as moving defects. However, model adaptivity is challenging because large particle motion is described based on a reference mesh (even in the atomistic regions). Unlike in the context of, for example, finite element meshes, adaptivity here requires that (i) all vertices lie on a discrete point set (the atomic lattice), (ii) model refinement is performed locally and provides sufficient mesh quality, and (iii) Verlet neighborhood updates in the atomistic domain are performed against a Lagrangian mesh. With the suite of adaptivity tools outlined here, the nonlocal QC method is shown to bridge across scales from atomistics to the continuum in a truly seamless fashion, as illustrated for nanoindentation and void growth. Copyright © 2016 John Wiley & Sons, Ltd.

We propose a highly effective approach using a novel adaptive methodology to perform topology optimization with polygonal meshes, called polytree meshes. Polytree is a hierarchical data structure based on the principle of recursive spatial decomposition of each polygonal element with *n* nodes into (*n* + 1) arbitrary new polygonal elements; enabling more efficient utilization of unstructured meshes and arbitrary design domains in topology optimization. In order to treat hanging nodes after each optimization loop, we define the Wachspress coordinate on a reference element and then utilize an affine map to obtain shape functions and their gradients on arbitrary polygons with *n* vertices and *m* hanging nodes, called side-nodes, as the polygonal element with (*n* + *m*) vertices. The polytree meshes do not only improve the boundary description quality of the optimal result but also reduce the computational cost of optimization process in comparison with the use of uniformly fine meshes. Several numerical examples are investigated to show the high effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

No abstract is available for this article.

]]>In nonlinear model order reduction, hyper reduction designates the process of approximating a projection-based reduced-order operator on a reduced mesh, using a numerical algorithm whose computational complexity scales with the small size of the projection-based reduced-order model. Usually, the reduced mesh is constructed by sampling the large-scale mesh associated with the high-dimensional model underlying the projection-based reduced-order model. The sampling process itself is governed by the minimization of the size of the reduced mesh for which the hyper reduction method of interest delivers the desired accuracy for a chosen set of training reduced-order quantities. Because such a construction procedure is combinatorially hard, its key objective function is conveniently substituted with a convex approximation. Nevertheless, for large-scale meshes, the resulting mesh sampling procedure remains computationally intensive. In this paper, three different convex approximations that promote sparsity in the solution are considered for constructing reduced meshes that are suitable for hyper reduction and paired with appropriate active set algorithms for solving the resulting minimization problems. These algorithms are equipped with carefully designed parallel computational kernels in order to accelerate the overall process of mesh sampling for hyper reduction, and therefore achieve practicality for realistic, large-scale, nonlinear structural dynamics problems. Conclusions are also offered as to what algorithm is most suitable for constructing a reduced mesh for the purpose of hyper reduction. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamic fragmentation is a rapid and catastrophic failure of a material. During this process, the nucleation, propagation, branching, and coalescence of cracks results in the formation of fragments. The numerical modeling of this phenomenon is challenging because it requires high-performance computational capabilities. For this purpose, the finite-element method with dynamic insertion of cohesive elements was chosen. This paper describes the parallel implementation of its fundamental algorithms in the C++ open-source library Akantu. Moreover, a numerical instability that can cause the loss of energy conservation and possible solutions to it are illustrated. Finally, the method is applied to the dynamic fragmentation of a hollow sphere subjected to uniform radial expansion. Copyright © 2016 John Wiley & Sons, Ltd.

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

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