Showing papers in "International Journal for Numerical Methods in Engineering in 2012"

Nonlinear model order reduction based on local reduced-order bases

Abstract: SUMMARY A new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced-order bases is presented. It is particularly suited for problems characterized by different physical regimes, parameter variations, or moving features such as discontinuities and fronts. Instead of approximating the solution of interest in a fixed lower-dimensional subspace of global basis vectors, the proposed model order reduction method approximates this solution in a lower-dimensional subspace generated by most appropriate local basis vectors. To this effect, the solution space is partitioned into subregions, and a local reduced-order basis is constructed and assigned to each subregion offline. During the incremental solution online of the reduced problem, a local basis is chosen according to the subregion of the solution space where the current high-dimensional solution lies. This is achievable in real time because the computational complexity of the selection algorithm scales with the dimension of the lower-dimensional solution space. Because it is also applicable to the process of hyper reduction, the proposed method for nonlinear model order reduction is computationally efficient. Its potential for achieving large speedups while maintaining good accuracy is demonstrated for two nonlinear computational fluid and fluid-structure-electric interaction problems. Copyright © 2012 John Wiley & Sons, Ltd.

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Abstract: SUMMARY In 3D fracture modeling, the complexity of the evolving crack geometry during propagation raises challenges in stress analysis because the accuracy of results mainly relies on the accurate description of the crack geometry. In this paper, a numerical framework is developed for 3D fracture modeling where a meshless method, the element-free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution. In this framework, a simple and general formulation for associating the displacement jump in the field approximation with an arbitrary 3D curved crack surface is proposed. For accurate closure of the crack front, a tying procedure is extended to 3D from its original use in 2D in the previous paper by the authors. The benefits of level sets in improving the results accuracy and reducing the computational cost are explored, particularly in the model refinement and the confinement of the displacement jump. Issues arising in level sets updating are discussed and solutions proposed accordingly. The developed framework is validated with a number of 3D crack examples with reference solutions and shows strong potential for general 3D fracture modeling. Copyright © 2012 John Wiley & Sons, Ltd.

Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach

Abstract: SUMMARY This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones. Copyright © 2012 John Wiley & Sons, Ltd.

Extended isogeometric analysis for simulation of stationary and propagating cracks

Abstract: SUMMARY A novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results. Copyright © 2011 John Wiley & Sons, Ltd.

Stabilization of projection-based reduced-order models

Abstract: SUMMARY A rigorous method for stabilizing projection-based linear reduced-order models without significantly affecting their accuracy is proposed. Unlike alternative approaches, this method is computationally efficient. It requires primarily the solution of a small-scale convex optimization problem. Furthermore, it is nonintrusive in the sense that it operates directly on readily available reduced-order operators. These can be precomputed using any data compression technique including balanced truncation, balanced proper orthogonal decomposition, proper orthogonal decomposition, or moment matching. The proposed method is illustrated with three applications: the stabilization of the reduction of the Computational Fluid Dynamics-based model of a linearized unsteady supersonic flow, the reduction of a Computational Structural Dynamics system, and the stabilization of the reduction of a coupled Computational Fluid Dynamics–Computational Structural Dynamics model of a linearized aeroelastic system in the transonic flow regime. Copyright © 2012 John Wiley & Sons, Ltd.

Polygon scaled boundary finite elements for crack propagation modelling

Abstract: SUMMARY An automatic crack propagation modelling technique using polygon elements is presented A simple algorithm to generate a polygon mesh from a Delaunay triangulated mesh is implemented The polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks Stress intensity factors are computed directly from their definitions without any nodal enrichment functions An automatic remeshing algorithm capable of handling any n-sided polygon is developed to accommodate crack propagation The algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths The efficiency of the polygon SBFEM in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack Four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features The predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature Copyright © 2012 John Wiley & Sons, Ltd

A polarization based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

Abstract: It is recognized that the convergence of FFT based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions, but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress based approaches. In this paper, we propose a new polarization-based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples.

A robust weakly compressible SPH method and its comparison with an incompressible SPH

Abstract: This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering-induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods.

Blossom-Quad: A non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm

Abstract: A new indirect way of producing all-quad meshes is presented. The method takes advantage of a wellknown algorithm of the graph theory, namely the Blossom algorithm, that computes the minimum-cost perfect matching in a graph in polynomial time. The new Blossom-Quad algorithm is compared with standard indirect procedures. Meshes produced by the new approach are better both in terms of element shape and in terms of size field efficiency.

An eigenerosion approach to brittle fracture

Abstract: The present work is concerned with the verification and validation of a variant of the eigenfracture scheme of Schmidt et al. (2009) based on element erosion, which we refer to as eigenerosion. Eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense: they can be either zero, in which case the local behavior is elastic, or they can be equal to the local displacement gradient, in which case the corresponding material neighborhood is failed or eroded. When combined with a finite-element approximation, this scheme gives rise to element erosion, i.e., the elements can be either intact, in which case their behavior is elastic, or be completly failed, or eroded, and have no load bearing capacity. We verify the eigenerosion scheme through comparisons with analytical solutions and through convergence studies for mode I fracture propagation, both in two and three dimensions and for structured and random meshes. Finally, by way of validation, we apply the eigenerosion scheme to the simulation of mixed modes I–III experiments in poly-methyl methacrylate plates.

Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description

Abstract: SUMMARY A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward. Copyright © 2011 John Wiley & Sons, Ltd.

A bi‐value coding parameterization scheme for the discrete optimal orientation design of the composite laminate

Abstract: SUMMARY The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by using the concept of continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme of closed form is proposed to this aim. The basic idea of the BCP scheme is to ‘code’ each material phase using integer values of +1 and –1 so that each available material phase has one unique ‘code’ consisting of +1 and/or –1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. The benefit is particularly remarkable when the number of candidate materials becomes important in large-scale problems. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the BCP scheme in solving this kind of problem. It proves that the BCP is an interesting and valuable scheme to achieve the optimal orientations for large-scale design problems. Besides, a four-layer laminate example is tested to demonstrate that the proposed BCP scheme can easily be extended to multilayer problems. Copyright © 2012 John Wiley & Sons, Ltd.

A reconstruction algorithm for electrical impedance tomography based on sparsity regularization

Abstract: SUMMARY This paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements. The sparsity of the ‘inhomogeneity’ with respect to a certain basis is a priori assumed. The proposed approach is motivated by a Tikhonov functional incorporating a sparsity-promoting l1-penalty term, and it allows us to obtain quantitative results when the assumption is valid. A novel iterative algorithm of soft shrinkage type was proposed. Numerical results for several two-dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization. Copyright © 2011 John Wiley & Sons, Ltd.

The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics

Abstract: SUMMARY The finite cell method (FCM) combines the fictitious domain approach with the p-version of the finite element method and adaptive integration. For problems of linear elasticity, it offers high convergence rates and simple mesh generation, irrespective of the geometric complexity involved. This article presents the integration of the FCM into the framework of nonlinear finite element technology. However, the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map. As a consequence of the weak penalization, nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries, leading to a low algebraic rate of convergence. Therefore, the FCM approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp-d method, which synergetically uses the h-adaptivity of the integration scheme. Numerical experiments show that the hp-d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map. The hp-d-adaptive FCM is thus able to restore high convergence rates for the geometrically nonlinear case, while preserving the easy meshing property of the original FCM. Accuracy and performance of the present scheme are demonstrated by several benchmark problems in one, two, and three dimensions and the nonlinear simulation of a complex foam sample. Copyright © 2011 John Wiley & Sons, Ltd.

Novel boundary conditions for strain localization analyses in microstructural volume elements

Abstract: SUMMARY Multi-scale modeling frequently relies on microstructural representative volume elements (RVEs) on which macroscopic deformation is imposed through kinematical boundary conditions. A particular choice of these boundary conditions may influence the obtained effective properties. For strain localization and damage analyses, the RVE is pushed beyond the limits of its representative character, and the applied boundary conditions have a significant impact on the onset and the type of macroscopic material instability to be predicted. In this article, we propose a new type of boundary conditions for microstructural volume elements, called percolation-path-aligned boundary conditions. Intrinsically, these boundary conditions capture the constraining effect of the material surrounding the RVE upon developing localization bands. The alignment with evolving localization bands allows the highly strained band to cross the RVE and fully develop with minimal interference of the applied boundary conditions. For an illustration of the performance of the newly proposed boundary conditions, macroscopic deformation has been imposed on a voided elasto-plastic RVE using different types of boundary conditions. It is observed that the new RVE boundary conditions provide a good estimate for the effective stiffness, are not susceptible to spurious localization, and permit the development of a full strain localization band up to failure. Copyright © 2011 John Wiley & Sons, Ltd.

An interface-enriched generalized FEM for problems with discontinuous gradient fields

Abstract: SUMMARY A new generalized FEM is introduced for solving problems with discontinuous gradient fields. The method relies on enrichment functions associated with generalized degrees of freedom at the nodes generated from the intersection of the phase interface with element edges. The proposed approach has several advantages over conventional generalized FEM formulations, such as a lower computational cost, easier implementation, and straightforward handling of Dirichlet boundary conditions. A detailed convergence study of the proposed method and a comparison with the standard FEM are presented for heat transfer problems. The method achieves the optimal rate of convergence using meshes that do not conform to the interfaces present in the domain while achieving a level of accuracy comparable to that of the standard FEM with conforming meshes. Various application problems are presented, including the conjugate heat transfer problem encountered in microvascular materials. Copyright © 2011 John Wiley & Sons, Ltd.

A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates

Abstract: SUMMARY The cell-based strain smoothing technique is combined with discrete shear gap method using three-node triangular elements to give a so-called cell-based smoothed discrete shear gap method (CS-DSG3) for static and free vibration analyses of Reissner–Mindlin plates. In the process of formulating the system stiffness matrix of the CS-DSG3, each triangular element will be divided into three subtriangles, and in each subtriangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole the triangular element is used to smooth the strains on these three subtriangles. The numerical examples demonstrated that the CS-DSG3 is free of shear locking, passes the patch test, and shows four superior properties such as: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) can give high accurate solutions for problems with skew geometries in the static analysis; (3) can give high accurate solutions in free vibration analysis; and (4) can provide accurately the values of high frequencies of plates by using only coarse meshes. Copyright © 2012 John Wiley & Sons, Ltd.

Proper generalized decomposition of time-multiscale models

Abstract: SUMMARY Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies. In some cases, the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval. In this paper, we considered an alternative approach that lies in separating the time axis (one-dimensional in nature) in a multidimensional time space. Then, for circumventing the resulting curse of dimensionality, the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration. Copyright © 2011 John Wiley & Sons, Ltd.

Coupling of nonlocal and local continuum models by the Arlequin approach

Abstract: SUMMARY The objective of this work is to develop and apply the Arlequin framework to couple nonlocal and local continuum mechanical models. A mechanically-based model of nonlocal elasticity, which involves both contact and long-range forces, is used for the ‘fine scale’ description in which nonlocal interactions are considered to have non-negligible effects. Classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can be neglected. Both models overlap in a coupling subdomain called the ‘gluing area’ in which the total energy is separated into nonlocal and local contributions by complementary weight functions. A weak compatibility is ensured between kinematics of both models using Lagrange multipliers over the gluing area. The discrete formulation of this specific Arlequin coupling framework is derived and fully described. The validity and limits of the technique are demonstrated through two-dimensional numerical applications and results are compared against those of the fully nonlocal elasticity method. Copyright © 2011 John Wiley & Sons, Ltd.

A modified scaled boundary finite element method for three‐dimensional dynamic soil‐structure interaction in layered soil

Abstract: SUMMARY This paper is devoted to the analysis of elastodynamic problems in 3D-layered systems which are unbounded in the horizontal direction. For this purpose, a finite element model of the near field is coupled to a scaled boundary finite element model (SBFEM) of the far field. The SBFEM is originally based on describing the geometry of a half-space or full-space domain by scaling the geometry of the near field / far field interface using a radial coordinate. A modified form of the SBFEM for waves in a 2D layer is also available. None of these existing formulations can be used to describe a 3D-layered medium. In this paper, a modified SBFEM for the analysis of 3D-layered continua is derived. Based on the use of a scaling line instead of a scaling centre, a suitable scaled boundary transformation is proposed. The derivation of the corresponding scaled boundary finite element (SBFE) equations in displacement and stiffness is presented in detail. The latter is a nonlinear differential equation with respect to the radial coordinate, which has to be solved numerically for each excitation frequency considered in the analysis. Various numerical examples demonstrate the accuracy of the new method and its correct implementation. These include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3D soil deposits over rigid bedrock. Hysteretic damping is assumed in some cases. The dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results. Copyright © 2011 John Wiley & Sons, Ltd.

Robust imposition of Dirichlet boundary conditions on embedded surfaces

Abstract: SUMMARY We develop both stable and stabilized methods for imposing Dirichlet constraints on embedded, three- dimensional surfaces in finite elements.The stable method makes use of the vital vertex algorithm of Bechet et al. (Bechet et al., 2009. Int. J. Numer. Meth. Engng. 78 (8), 931-954), albeit with a modified set of discontinuous basis functions for the Lagrange multiplier field on the embedded surface. The stabilized method extends the work of Dolbow and Harari (Dolbow and Harari, 2009. Int. J. Numer. Meth. Engng. 78 (2), 229-252) to three-dimensional surfaces. Algorithmic and implementational details of both methods are provided. Several three-dimensional benchmark problems are studied to compare and contrast the accuracy of the two approaches. The results indicate that both methods yield optimal rates of convergence in various quantities of interest, with the primary differences being in the surface flux. The utility of the domain integral for extracting accurate surface fluxes is demonstrated for both techniques. published by John Wiley & Sons Ltd. Copyright c 2000 John Wiley & Sons, Ltd.

Formulation and sequential numerical algorithms of coupled fluid/heat flow and geomechanics for multiple porosity materials

Abstract: Formulation and sequential numerical algorithms of coupled fluid/heat flow and geomechanics for multiple porosity materials J. Kim ∗ , E. Sonnenthal, and J. Rutqvist Earth Sciences Division, Lawrence Berkeley National Laboratory. 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA SUMMARY We generalized constitutive relations of coupled flow and geomechanics for the isothermal elastic double porosity model in the previous study to those for the non-isothermal elastic/elastoplastic multiple porosity model, finding coupling coefficients and constraints of the multiple porosity model, and determining the upscaled elastic/elastoplastic moduli as well as relations between the local strains of all materials within a gridblock and the global strain of the gridblock. Furthermore, the coupling equations and relations between local and global variables provide well-posed problems, implying that they honor the dissipative mechanism of coupled flow and geomechanics. For numerical implementation, we modified the fixed-stress sequential method for the multiple porosity model. From the a priori stability estimate, the sequential method provides numerical stability when an implicit time stepping algorithm is used. This sequential scheme can easily be implemented by using a modified porosity function and its porosity correction. In numerical examples, we observe clear differences among the single, double, and multiple porosity systems, and the multiple porosity model can reflect high heterogeneity that exists within a gridblock. We also identify considerably complicated physics in coupled flow and geomechanics of the multiple porosity systems, which cannot accurately be detected in the uncoupled flow simulation. KEY WORDS: double porosity, multiple porosity, poromechanics, multiple interacting continua (MINC), fractured reservoirs, fixed-stress split 1. INTRODUCTION Coupled fluid, heat, and mechanical processes are important in many engineering fileds. In mechanical engineering, coupled heat and mechanics (e.g., thermoelasticity, thermoplasticity) are considered to analyze interactions between deformation of a material body and thermal stress [1, 2]. Rapid movement of the body such as vibration can be a source in heat flow, and heat induces additional stress in mechanics, which can expand the body. In turn, the expanded body affects accumulation in heat flow because of the change in material volume. Coupled fluid, heat, and mechanical processes are also critically important in geo-engineering [3]. In geotechnical engineering, an increase (or decrease) of pore pressure causes dilation (or shrinkage) of porous media, which changes strain and stress fields [4, 5, 6, 7, 8]. These changes also affect pore-volume, resulting in variation of pore-pressure, again. In petroleum engineering, changes in permeability as well as porosity induced by geomechanics are critical issues in order to predict fluid flow and production accurately, for example, in hydraulic fracturing, reservoir compaction, and gas-hydrate recovery [9, 10, 11, 12, 13, 14]. In geological carbon storage, the effect of large scale injection ∗ Correspondence to: J. Kim, Earth Sciences Division, Lawrence Berkeley National Laboratory. 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA. Email: JihoonKim@lbl.gov

Computation of limit and shakedown loads using a node‐based smoothed finite element method

Abstract: SUMMARY This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods. Copyright © 2011 John Wiley & Sons, Ltd.

A unified 3D‐based technique for plate bending analysis using scaled boundary finite element method

Abstract: SUMMARY This paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method. The formulation is based on the three-dimensional governing equation without enforcing the kinematics of plate theory. Only the in-plane dimensions are discretised into finite elements. Any two-dimensional displacement-based elements can be employed. The solution along the thickness is expressed analytically by using a matrix function. The proposed technique is consistent with the three-dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon. Moreover, the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence. Numerical examples of various plate structures with different thickness-to-length ratios demonstrate the applicability and accuracy of the proposed technique. Copyright © 2012 John Wiley & Sons, Ltd.

Computational homogenization for multiscale crack modeling. Implementational and computational aspects

Abstract: A computational homogenization procedure for cohesive and adhesive crack modeling of materials with a heterogeneous microstructure has been recently presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013). The macroscopic material properties of the cohesive cracks are obtained from the inelastic deformation manifested in a localization band (modeled with a continuum damage theory) at the microscopic scale. The macroscopic behavior of the adhesive crack is derived from the response of a microscale sample representing the microstructure inside the adhesive crack. In this manuscript, we extend the theory presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013) with implementation details, solutions for cyclic loading, crack propagation, numerical analysis of the convergence characteristics of the multiscale method, and treatment of macroscopic snapback in a multiscale simulation. Numerical examples including crack growth simulations with extended finite elements are given to demonstrate the performance of the method.

Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling

Abstract: SUMMARY Design of reinforced concrete structures is governed by the nonlinear behavior of concrete and by its different strengths in tension and compression. The purpose of this article is to present a computational procedure for optimal conceptual design of reinforced concrete structures on the basis of topology optimization with elastoplastic material modeling. Concrete and steel are both considered as elastoplastic materials, including the appropriate yield criteria and post-yielding response. The same approach can be applied also for topology optimization of other material compositions where nonlinear response must be considered. Optimized distribution of materials is achieved by introducing interpolation rules for both elastic and plastic material properties. Several numerical examples illustrate the capability and potential of the proposed procedure. Copyright © 2012 John Wiley & Sons, Ltd.

Computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis

Abstract: This paper is devoted to the computational nonlinear stochastic homogenization of a hyperelastic heterogeneous microstructure using a non-concurrent multiscale approach. The geometry of the microstructure is random. Since the non-concurrent multiscale approach is based on the use of a tensorial decomposition, which is then submitted to the curse of dimensionality, we perform an analysis with respect to the stochastic dimension. The technique uses a database describing the strain energy density function (potential) in both the macroscopic Cauchy Green strain space and the geometrical random parameters domain. Each value of the potential is numerically computed by means of the finit element method on an elementary cell. An interpolation scheme is finall introduced to obtain a continuous explicit form of the potential, which, by derivation, allows to evaluate the macroscopic stress and elastic tangent tensors during the macroscopic structural computations. Two numerical examples are presented

Parameter multi‐domain ‘hp’ empirical interpolation

Abstract: SUMMARY In this paper, we introduce two parameter multi-domain ‘ hp’ techniques for the empirical interpolation method (EIM). In both approaches, we construct a partition of the original parameter domain into parameter subdomains: h-refinement. We apply the standard EIM independently within each subdomain to yield local (in parameter) approximation spaces: p-refinement. Further, for a particularly simple case, we introduce a priori convergence theory for the partition procedure. We show through two numerical examples that our approaches provide significant reduction in the EIM approximation space dimension and thus significantly reduce the computational cost associated with EIM approximations. Copyright © 2012 John Wiley & Sons, Ltd.

Regularized integral equations and fast high‐order solvers for sound‐hard acoustic scattering problems

Abstract: This text introduces the following: (1) new regularized combined field integral equations (CFIE-R) for frequency-domain sound-hard scattering problems; and (2) fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Similar to the classical combined field integral equation (CFIE), the CFIE-R are uniquely-solvable integral equations based on the use of single and double layer potentials. Unlike the CFIE, however, the CFIE-R utilize a composition of the double-layer potential with a regularizing operator that gives rise to highly favorable spectral properties—thus making it possible to produce accurate solutions by means of iterative solvers in small numbers of iterations. The CFIE-R-based fast high-order integral algorithms introduced in this text enable highly accurate solution of challenging sound-hard scattering problems, including hundred-wavelength cases, in single-processor runs on present-day desktop computers. A variety of numerical results demonstrate the qualities of the numerical solvers as well as the advantages that arise from the new integral equation formulation.