Authors:Shuhai Zhang; Caglar Oskay Pages: 887 - 907 Abstract: This manuscript presents the formulation and implementation of the reduced order variational multiscale enrichment (ROVME) method for thermo-mechanical problems. ROVME is extended to model the inelastic behavior of heterogeneous structures, in which the constituent properties are temperature sensitive. The temperature-dependent coefficient tensors of the reduced order method are approximated in an efficient manner, retaining the computational efficiency of the reduced order model in the presence of spatial/temporal temperature variations. A Newton–Raphson iterative scheme is formulated and implemented for the numerical evaluation of nonlinear system of equations associated with the proposed ROVME method. Numerical verifications are performed to assess the efficiency and accuracy of the proposed computational framework. The results of the verifications reveal that ROVME retains reasonable accuracy and achieves high efficiency in the presence of hermo-mechanical loads. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1380-9 Issue No:Vol. 59, No. 6 (2017)

Authors:Hao Li; Pierre Ladeveze; Hervé Riou Pages: 909 - 918 Abstract: In the past years, a numerical technique method called Variational Theory of Complex Rays (VTCR) has been developed for vibration problems in medium frequency. It is a Trefftz Discontinuous Galerkin method which uses plane wave functions as shape functions. However this method is only well developed in homogeneous case. In this paper, VTCR is extended to the heterogeneous Helmholtz problem by creating a new base of shape functions. Numerical examples give a scope of the performances of such an extension of VTCR. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1385-4 Issue No:Vol. 59, No. 6 (2017)

Authors:S. Sadamoto; M. Ozdemir; S. Tanaka; K. Taniguchi; T. T. Yu; T. Q. Bui Pages: 919 - 932 Abstract: The paper is concerned with eigen buckling analysis of curvilinear shells with and without cutouts by an effective meshfree method. In particular, shallow shell, cylinder and perforated cylinder buckling problems are considered. A Galerkin meshfree reproducing kernel (RK) approach is then developed. The present meshfree curvilinear shell model is based on Reissner-Mindlin plate formulation, which allows the transverse shear deformation of the curved shells. There are five degrees of freedom per node (i.e., three displacements and two rotations). In this setting, the meshfree interpolation functions are derived from the RK. A singular kernel is introduced to impose the essential boundary conditions because of the RK shape functions, which do not automatically possess the Kronecker delta property. The stiffness matrix is derived using the stabilized conforming nodal integration technique. A convected coordinate system is introduced into the formulation to deal with the curvilinear surface. More importantly, the RKs taken here are used not only for the interpolation of the curved geometry, but also for the approximation of field variables. Several numerical examples with shallow shells and full cylinder models are considered, and the critical buckling loads and their buckling mode shapes are calculated by the meshfree eigenvalue analysis and examined. To show the accuracy and performance of the developed meshfree method, the computed critical buckling loads and mode shapes are compared with reference solutions based on boundary domain element, finite element and analytical methods. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1384-5 Issue No:Vol. 59, No. 6 (2017)

Authors:Charles Dapogny; Alexis Faure; Georgios Michailidis; Grégoire Allaire; Agnes Couvelas; Rafael Estevez Pages: 933 - 965 Abstract: This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1383-6 Issue No:Vol. 59, No. 6 (2017)

Authors:Yangjun Luo; Yanzhuang Niu; Ming Li; Zhan Kang Pages: 967 - 980 Abstract: In order to eliminate stress-related wrinkles in cable-suspended membrane structures and to provide simple and reliable deployment, this study presents a multi-material topology optimization model and an effective solution procedure for generating optimal connected layouts for membranes and cables. On the basis of the principal stress criterion of membrane wrinkling behavior and the density-based interpolation of multi-phase materials, the optimization objective is to maximize the total structural stiffness while satisfying principal stress constraints and specified material volume requirements. By adopting the cosine-type relaxation scheme to avoid the stress singularity phenomenon, the optimization model is successfully solved through a standard gradient-based algorithm. Four-corner tensioned membrane structures with different loading cases were investigated to demonstrate the effectiveness of the proposed method in automatically finding the optimal design composed of curved boundary cables and wrinkle-free membranes. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1387-2 Issue No:Vol. 59, No. 6 (2017)

Authors:J. Reinoso; M. Paggi; C. Linder Pages: 981 - 1001 Abstract: Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1386-3 Issue No:Vol. 59, No. 6 (2017)

Authors:M. Davari; R. Rossi; P. Dadvand Pages: 1003 - 1030 Abstract: The present paper explores the solution of a heat conduction problem considering discontinuities embedded within the mesh and aligned at arbitrary angles with respect to the mesh edges. Three alternative approaches are proposed as solutions to the problem. The difference between these approaches compared to alternatives, such as the eXtended Finite Element Method (X-FEM), is that the current proposal attempts to preserve the global matrix graph in order to improve performance. The first two alternatives comprise an enrichment of the Finite Element (FE) space obtained through the addition of some new local degrees of freedom to allow capturing discontinuities within the element. The new degrees of freedom are statically condensed prior to assembly, so that the graph of the final system is not changed. The third approach is based on the use of modified FE-shape functions that substitute the standard ones on the cut elements. The imposition of both Neumann and Dirichlet boundary conditions is considered at the embedded interface. The results of all the proposed methods are then compared with a reference solution obtained using the standard FE on a mesh containing the actual discontinuity. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1382-7 Issue No:Vol. 59, No. 6 (2017)

Authors:A. Pagani; A. G. de Miguel; E. Carrera Pages: 1031 - 1048 Abstract: This paper discusses the use of higher-order mapping functions for enhancing the physical representation of refined beam theories. Based on the Carrera unified formulation (CUF), advanced one-dimensional models are formulated by expressing the displacement field as a generic expansion of the generalized unknowns. According to CUF, a novel physically/geometrically consistent model is devised by employing Legendre-like polynomial sets to approximate the generalized unknowns at the cross-sectional level, whereas a local mapping technique based on the blending functions method is used to describe the exact physical boundaries of the cross-section domain. Classical and innovative finite element methods, including hierarchical p-elements and locking-free integration schemes, are utilized to solve the governing equations of the unified beam theory. Several numerical applications accounting for small displacements/rotations and strains are discussed, including beam structures with cross-sectional curved edges, cylindrical shells, and thin-walled aeronautical wing structures with reinforcements. The results from the proposed methodology are widely assessed by comparisons with solutions from the literature and commercial finite element software tools. The attention is focussed on the high computational efficiency and the marked capabilities of the present beam model, which can deal with a broad spectrum of structural problems with unveiled accuracy in terms of geometrical representation of the domain boundaries. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1390-7 Issue No:Vol. 59, No. 6 (2017)

Authors:D. Feng; I. Neuweiler; U. Nackenhorst Pages: 1049 - 1070 Abstract: We consider a model for biofilm growth in the continuum mechanics framework, where the growth of different components of biomass is governed by a time dependent advection–reaction equation. The recently developed time-discontinuous Galerkin (TDG) method combined with two different stabilization techniques, namely the Streamline Upwind Petrov Galerkin (SUPG) method and the finite increment calculus (FIC) method, are discussed as solution strategies for a multi-dimensional multi-species biofilm growth model. The biofilm interface in the model is described by a convective movement following a potential flow coupled to the reaction inside of the biofilm. Growth limiting substrates diffuse through a boundary layer on top of the biofilm interface. A rolling ball method is applied to obtain a boundary layer of constant height. We compare different measures of the numerical dissipation and dispersion of the simulation results in particular for those with non-trivial patterns. By using these measures, a comparative study of the TDG–SUPG and TDG–FIC schemes as well as sensitivity studies on the time step size, the spatial element size and temporal accuracy are presented. PubDate: 2017-06-01 DOI: 10.1007/s00466-017-1388-1 Issue No:Vol. 59, No. 6 (2017)

Authors:J. P. Whiteley Abstract: Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton’s method. On each iteration of Newton’s method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems. PubDate: 2017-06-20 DOI: 10.1007/s00466-017-1430-3

Authors:Miguel Arriaga; Haim Waisman Abstract: A local physical stability criterion for multidimensional fracture problems modeled by the phase field method is developed and studied. Stability analysis provides a rigorous mathematical way to determine the onset of an unstable damage growth and fracture of the structure. In this work, stability is determined by examining the roots of a characteristic equation that arise when a linear perturbation technique is applied to the instantaneous partial differential equation system in a general viscoplastic material. It is shown that such analysis is not limited to a particular degradation function or energy split and could therefore be applied to a wide range of cases. Numerical results are presented to verify the theoretical predictions assuming quadratic and cubic degradation functions. Additionally we show that this stability criterion can be directly expanded to 2D with robust mesh-insensitive predictive capabilities with respect to crack nucleation and path. Several numerical examples are presented to verify these results. PubDate: 2017-06-17 DOI: 10.1007/s00466-017-1432-1

Authors:E. Artioli; L. Beirão da Veiga; C. Lovadina; E. Sacco Abstract: The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi:10.1007/s00466-017-1404-5), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework. PubDate: 2017-06-14 DOI: 10.1007/s00466-017-1429-9

Authors:Steffen Beese; Stefan Loehnert; Peter Wriggers Abstract: In this contribution we present a gradient enhanced damage based method to simulate discrete crack propagation in 3D polycrystalline microstructures. Discrete cracks are represented using the eXtended finite element method. The crack propagation criterion and the crack propagation direction for each point along the crack front line is based on the gradient enhanced damage variable. This approach requires the solution of a coupled problem for the balance of momentum and the additional global equation for the gradient enhanced damage field. To capture the discontinuity of the displacements as well as the gradient enhanced damage along the discrete crack, both fields are enriched using the XFEM in combination with level sets. Knowing the crack front velocity, level set methods are used to compute the updated crack geometry after each crack propagation step. The applied material model is a crystal plasticity model often used for polycrystalline microstructures of metals in combination with the gradient enhanced damage model. Due to the inelastic material behaviour after each discrete crack propagation step a projection of the internal variables from the old to the new crack configuration is required. Since for arbitrary crack geometries ill-conditioning of the equation system may occur due to (near) linear dependencies between standard and enriched degrees of freedom, an XFEM stabilisation technique based on a singular value decomposition of the element stiffness matrix is proposed. The performance of the presented methodology to capture crack propagation in polycrystalline microstructures is demonstrated with a number of numerical examples. PubDate: 2017-06-13 DOI: 10.1007/s00466-017-1427-y

Authors:Erik Svenning; Fredrik Larsson; Martin Fagerström Abstract: We consider multiscale modeling of fracturing solids undergoing strain localization, whereby Statistical Volume Elements (SVEs) are used to compute the homogenized macroscopic stresses and the eXtended Finite Element Method (XFEM) is used to represent macroscale displacement discontinuities. These discontinuities are imposed on the localized SVEs in a smeared sense, whereby the smearing width is related to the SVE size and the orientation of the macroscopic discontinuity. This smearing width relation, which is derived within the setting of Variationally Consistent Homogenization (VCH), prevents pathological dependence of the solution on the SVE size. The SVE size insensitivity is further improved by adopting the recently proposed localization aligned weakly periodic boundary conditions. Advantages of the proposed method are that it allows multiscale modeling of localized fracture without restrictive assumptions on the SVE size and without the need to explicitly track a localized region in the SVE. PubDate: 2017-06-12 DOI: 10.1007/s00466-017-1426-z

Authors:Dominic Soldner; Benjamin Brands; Reza Zabihyan; Paul Steinmann; Julia Mergheim Abstract: Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model. PubDate: 2017-06-08 DOI: 10.1007/s00466-017-1428-x

Authors:Niels Goldberg; Felix Ospald; Matti Schneider Abstract: In this article we introduce a fiber orientation-adapted integration scheme for Tucker’s orientation averaging procedure applied to non-linear material laws, based on angular central Gaussian fiber orientation distributions. This method is stable w.r.t. fiber orientations degenerating into planar states and enables the construction of orthotropic hyperelastic energies for truly orthotropic fiber orientation states. We establish a reference scenario for fitting the Tucker average of a transversely isotropic hyperelastic energy, corresponding to a uni-directional fiber orientation, to microstructural simulations, obtained by FFT-based computational homogenization of neo-Hookean constituents. We carefully discuss ideas for accelerating the identification process, leading to a tremendous speed-up compared to a naive approach. The resulting hyperelastic material map turns out to be surprisingly accurate, simple to integrate in commercial finite element codes and fast in its execution. We demonstrate the capabilities of the extracted model by a finite element analysis of a fiber reinforced chain link. PubDate: 2017-06-07 DOI: 10.1007/s00466-017-1425-0

Authors:Yeo-Ul Song; Sung-Kie Youn; K. C. Park Abstract: A method for three-dimensional non-matching interface treatment with a virtual gap element is developed. When partitioned structures contain curved interfaces and have different brick meshes, the discretized models have gaps along the interfaces. As these gaps bring unexpected errors, special treatments are required to handle the gaps. In the present work, a virtual gap element is introduced to link the frame and surface domain nodes in the frame work of the mortar method. Since the surface of the hexahedron element is quadrilateral, the gap element is pyramidal. The pyramidal gap element consists of four domain nodes and one frame node. Zero-strain condition in the gap element is utilized for the interpolation of frame nodes in terms of the domain nodes. This approach is taken to satisfy the momentum and energy conservation. The present method is applicable not only to curved interfaces with gaps, but also to flat interfaces in three dimensions. Several numerical examples are given to describe the effectiveness and accuracy of the proposed method. PubDate: 2017-06-03 DOI: 10.1007/s00466-017-1423-2

Authors:Hauke Gravenkamp; Sascha Duczek Abstract: Quadtree-based domain decomposition algorithms offer an efficient option to create meshes for automatic image-based analyses. Without introducing hanging nodes the scaled boundary finite element method (SBFEM) can directly operate on such meshes by only discretizing the edges of each subdomain. However, the convergence of a numerical method that relies on a quadtree-based geometry approximation is often suboptimal due to the inaccurate representation of the boundary. To overcome this problem a combination of the SBFEM with the spectral cell method (SCM) is proposed. The basic idea is to treat each uncut quadtree cell as an SBFEM polygon, while all cut quadtree cells are computed employing the SCM. This methodology not only reduces the required number of degrees of freedom but also avoids a two-dimensional quadrature in all uncut quadtree cells. Numerical examples including static, harmonic, modal and transient analyses of complex geometries are studied, highlighting the performance of this novel approach. PubDate: 2017-06-02 DOI: 10.1007/s00466-017-1424-1

Authors:Shigeki Kaneko; Giwon Hong; Naoto Mitsume; Tomonori Yamada; Shinobu Yoshimura Abstract: Fluid–structure interaction (FSI) is an interdependent phenomenon between a fluid and a structure that affects their dynamic behavior. It is important because it often affects the safety and lifetime of structures. Therefore, controlling FSI is important. In the study of the control of FSI, numerical simulations are often used because they are suitable for parametric studies and reduce the need for experiments. A number of numerical studies have examined the control of FSI. However, existing numerical studies have rarely performed both fluid and structural analyses strictly and sufficiently treated interaction conditions on the coupling interface. Therefore, the types of FSI problems that can be analyzed are limited. In order to enable the treatment of a greater variety of FSI problems, it was necessary to develop a new method. The partitioned iterative method has succeeded in analyzing complicated FSI problems, and, in the present study, we propose FSI analysis considering active control by integrating FSI analysis by a partitioned iterative method and an active control algorithm. We explain the proposed method, and we validate the method by solving two-dimensional vortex-induced vibration (VIV) of an elastically mounted cylinder with active control of a velocity feedback. Furthermore, we present an application example by solving the suppression of two-dimensional VIV of a flexible structure in the wake of a bluff body. PubDate: 2017-05-27 DOI: 10.1007/s00466-017-1422-3

Authors:Somnath Ghosh; Jiahao Cheng Abstract: Crystal plasticity finite element (CPFE) models that accounts for discrete micro-twin nucleation-propagation have been recently developed for studying complex deformation behavior of hexagonal close-packed (HCP) materials (Cheng and Ghosh in Int J Plast 67:148–170, 2015, J Mech Phys Solids 99:512–538, 2016). A major difficulty with conducting high fidelity, image-based CPFE simulations of polycrystalline microstructures with explicit twin formation is the prohibitively high demands on computing time. High strain localization within fast propagating twin bands requires very fine simulation time steps and leads to enormous computational cost. To mitigate this shortcoming and improve the simulation efficiency, this paper proposes a multi-time-domain subcycling algorithm. It is based on adaptive partitioning of the evolving computational domain into twinned and untwinned domains. Based on the local deformation-rate, the algorithm accelerates simulations by adopting different time steps for each sub-domain. The sub-domains are coupled back after coarse time increments using a predictor-corrector algorithm at the interface. The subcycling-augmented CPFEM is validated with a comprehensive set of numerical tests. Significant speed-up is observed with this novel algorithm without any loss of accuracy that is advantageous for predicting twinning in polycrystalline microstructures. PubDate: 2017-05-23 DOI: 10.1007/s00466-017-1421-4