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See detailEffects of elastic strain energy and interfacial stress on the equilibrium morphology of misfit particles in heterogeneous solids
Zhao, X.; Duddu, R.; Bordas, Stéphane UL et al

in Journal of the Mechanics & Physics of Solids (2013), 61(6), 1433-1445

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are ... [more ▼]

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are considered. The geometry of the material interface is implicitly described by the level set method so that the complex morphological transformation of microstructures can be accurately captured. A smoothed extended finite element method is adopted to evaluate the elastic field without requiring remeshing. The equilibrium morphologies of particles are shown to depend on the elastic anisotropy, interfacial energy as well as the particle size. Various morphological transformations, such as shape changes from spheres to cuboids, directional aligned platelets and particle splitting, are observed. The simulated results are in good agreement with experimental observations. The proposed model provides a useful tool in understanding the morphological transformation of precipitates, which will facilitate the analysis and design of metallic alloys. © 2013 Elsevier Ltd. [less ▲]

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See detailStress analysis without meshing: Isogeometric boundary-element method
Lian, H.; Simpson, R. N.; Bordas, Stéphane UL

in Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics (2013), 166(2), 88-99

The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The ... [more ▼]

The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The clear benefit of the approach is that no mesh needs to be generated prior to running the analysis. This is achieved by utilising the isogeometric concept whereby computer-aided design data are used to construct not only the geometry discretisation but also the displacement and traction approximations. In this manner, significant savings can be made in the engineering design and analysis process. This paper also demonstrates that, compared with a standard boundary-element method implementation using quadratic Lagrangian shape functions, superior accuracy is achieved using the present approach for the same number of degrees of freedom. It further illustrates practical applications of the method, comparing against results obtained with a standard boundary-element method and finite-element method for verification. In addition, a propeller is analysed as a sample to show the ability of the present method to handle complex three-dimensional geometries. [less ▲]

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See detailThe Node-Based Smoothed Finite Element Method in nonlinear elasticity
Lee, Chang-Kye; Mihai, L. Angela; Bordas, Stéphane UL

Report (2013)

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See detailA partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
Kerfriden, P.; Goury, O.; Rabczuk, T. et al

in Computer Methods in Applied Mechanics & Engineering (2013), 256

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order ... [more ▼]

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. © 2012 Elsevier B.V. [less ▲]

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See detailThe virtual node polygonal element method for nonlinear thermal analysis with application to hybrid laser welding
Wu, SC; Peng, X; Zhang, WH et al

in International Journal of Heat & Mass Transfer (2013), 67

The nonlinear heat transfer process occurring during hybrid laser welding was simulated using the Virtual-node Polygonal Element (VPE) method within the framework of the Finite Element Method (FEM). To ... [more ▼]

The nonlinear heat transfer process occurring during hybrid laser welding was simulated using the Virtual-node Polygonal Element (VPE) method within the framework of the Finite Element Method (FEM). To achieve robustness in large-scale welding simulations, a dynamic mesh refinement with quadtree and octree data structures was used in the welding region. Accuracy, convergence and efficiency were verified by solving two and three dimensional problems. It is found that the present VPE can successfully simulate the hybrid laser welding process with good accuracy and convergence. The adaptive refined mesh box can synchronously move with the welding heat source, which dramatically reduces the number of field nodes. Compared with the standard FEM,the VPEM requires only approximately 42% of the total degrees of freedom used in standard FEM for the same accuracy. Furthermore, we compare the computational cost and accuracy of the method to that of the finite element method, the edge based virtual node polygonal element/virtual node method, the edge-based Smoothed Point Interpolation Meshless Method (ES-PIM), the edge-based Element (ES-PIM) the Element Free Galerkin (EFG) method and the Meshless Local Petrove-Galerkin Petrov-Galerkin (MLPG) method. Compared to all those methods, the proposed scheme is found competitive in terms of computational cost versus accuracy, and benefit from a simple implementation. © 2012 Elsevier B.V. All rights reserved. [less ▲]

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See detailAn Adaptive Multiscale Method for Quasi-static Crack Growth
Pattabhi, Budarapu; Robert, Gracie; Bordas, Stéphane UL et al

in Computational Mechanics (2013)

This paper proposes an adaptive atomistic-continuum numerical method for quasi-static <br />crack growth. The phantom node method is used to model the crack in the continuum region <br />and a molecular ... [more ▼]

This paper proposes an adaptive atomistic-continuum numerical method for quasi-static <br />crack growth. The phantom node method is used to model the crack in the continuum region <br />and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, <br />a virtual atom cluster is used to model the material of the coarse scale. The coupling between <br />the coarse scale and ne scale is realized through ghost atoms. The ghost atom positions are <br />interpolated from the coarse scale solution and enforced as boundary conditions on the ne <br />scale. The ne scale region is adaptively enlarged as the crack propagates and the region behind <br />the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip loca- <br />tion. The triangular lattice in the ne scale region corresponds to the lattice structure of the <br />(111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom-atom <br />interactions. The method is implemented in two dimensions. The results are compared to pure <br />atomistic simulations; they show excellent agreement. [less ▲]

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See detailSpace-time goal-oriented reduced basis approximation for linear wave equation
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

Report (2013)

In this paper, we study numerically the linear damped second-order hyperbolic partial differen-tial equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE ... [more ▼]

In this paper, we study numerically the linear damped second-order hyperbolic partial differen-tial equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the “goal-oriented” proper orthogonal decomposition (POD)–Greedy sampling procedure within the RB approximation context. First, we introduce the RB recipe: Galerkin projection onto a space YN spanned by solutions of the governing PDE at N selected points in parameter space. This set of N parameter points is constructed by the standard POD–Greedy sampling procedure already developed. Second, based on the affine parameter dependence, we make use of the offline-online computational procedures: in the offline stage, we generate the RB space; in the online stage, given a new parameter value, we calculate rapidly and accurately the space-time RB output of interest and its associated asymptotic error. The proposed goal-oriented POD–Greedy sampling procedure can now be implemented and will look for the parameter points such that it minimizes this (asymptotic) output error rather than the solution error (or, error indicator which is the dual norm of residual) as in the standard POD–Greedy procedure. Numerical results show that the new goal-oriented POD–Greedy sampling procedure improves significantly the accuracy of the space-time output computation in comparison with the standard POD–Greedy one. The method is thus ideally suited for repeated, rapid and reliable evaluation of input-output relationships within the space-time setting. [less ▲]

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See detailXLME interpolants, a seamless bridge between XFEM and enriched meshless methods
Amiri, F.; Anitescu, C.; Arroyo, M. et al

in Computational Mechanics (2013)

In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture ... [more ▼]

In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method at a comparable computational cost. In addition, we keep the advantages of the LME shape functions, such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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See detailAn isogeometric boundary element method for elastostatic analysis: 2D implementation aspects
Simpson, R. N.; Bordas, Stéphane UL; Lian, H. et al

in Computers & Structures (2013), 118

The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed ... [more ▼]

The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlining an isogeometric boundary element Method (IGABEM) that only requires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementations. Examples of Matlab® code are given whenever possible to aid understanding of the techniques used. [less ▲]

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See detailStable extended finite element method: Convergence, Accuracy, Properties and Diffpack implementation
Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013)

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally ... [more ▼]

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally opposed approaches are attempting to simplify the CAD to Analysis pipeline: isogeometric methods on the one hand [1] aim at coupling the geometry and field approximations, whilst implicit boundary definition-based methods attempt to decouple them [3,4,5]. We examine in this paper one instance of the latter approach, and rely on partition of unity enrichment of the field variable to capture discontinuities along material interface or domain boundaries. We study in particular the stable generalized finite element method of Babuˇka and Banerjee [6] for higher order approximations in two and three dimensions and propose a generic implementation within the C++ library Diffpack from inuTech GmbH [7]. In a companion paper, the implementation of enrichment within Diffpack is presented in more detail. We will present results obtained with our 3D implementation of partition of unity enrichment within Diffpack. This implementation represents the interfaces through level-sets and palliates blending problems using various approaches. We study here the stabilisation approach proposed in [6] in more detail and pay particular attention to the global convergence rate of the approach and to the stability and the local flux converence close to the interfaces. [less ▲]

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See detailAnalysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements
Natarajan, S.; Ferreira, Ana UL; Bordas, Stéphane UL et al

in Composite Structures (2013), 105

In this article, we combine Carrera's Unified Formulation (CUF) [13,7] and cell based smoothed finite element method [28] for studying the static bending and the free vibration of thin and thick laminated ... [more ▼]

In this article, we combine Carrera's Unified Formulation (CUF) [13,7] and cell based smoothed finite element method [28] for studying the static bending and the free vibration of thin and thick laminated plates. A 4-noded quadrilateral element based on the field consistency requirement is used for this study to suppress the shear locking phenomenon. The combination of cell based smoothed finite element method and field consistent approach with CUF allows a very accurate prediction of field variables. The accuracy and efficiency of the proposed approach are demonstrated through numerical experiments. © 2013 Elsevier Ltd. [less ▲]

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See detailA computational library for multiscale modeling of material failure
Talebi, H.; Silani, M.; Bordas, Stéphane UL et al

in Computational Mechanics (2013)

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran ... [more ▼]

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH. Fracture on the continuum level is modeled by the extended finite element method (XFEM). Using several novel or state of the art methods, the piece software handles semi-concurrent multiscale methods as well as concurrent multiscale methods for fracture, coupling two continuum domains or atomistic domains to continuum domains, respectively. The efficiency of our open-source software is shown through several simulations including a 3D crack modeling in clay nanocomposites, a semi-concurrent FE-FE coupling, a 3D Arlequin multiscale example and an MD-XFEM coupling for dynamic crack propagation. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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See detailStatistical extraction of process zones and representative subspaces in fracture of random composites
Kerfriden, P.; Schmidt, K. M.; Rabczuk, T. et al

in International Journal for Multiscale Computational Engineering (2013), 11(3), 253-287

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly ... [more ▼]

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model. © 2013 by Begell House, Inc. [less ▲]

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See detailImplementation of a XFEM toolbox in Diffpack
Hossain, Md Naim; Paladim, Daniel; Vogel, Frank et al

in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013)

The Diffpack Development Framework is an object-oriented software environment for the numerical solution of partial differential equations (PDEs). By its design, Diffpack intends to close the gap between ... [more ▼]

The Diffpack Development Framework is an object-oriented software environment for the numerical solution of partial differential equations (PDEs). By its design, Diffpack intends to close the gap between black-box simulation packages and technical computing environments using interpreted computer languages. The framework provides a high degree of modeling flexibility, while still offering the computational efficiency needed for most demanding simulation problems in science and engineering. Technically speaking, Diffpack is a collection of C++ libraries with classes, functions and utility programs. The numerical functionality is embedded in an environment of software engineering tools supporting the management of Diffpack development projects. Diffpack supports a variety of numerical methods with distinct focus on the finite element method (FEM) but has no inherent restrictions on the types of PDEs and therefore applications to be solved. The key point of partition of unity enriched methods such as XFEM and GFEM is to help capture discontinuities and singularities or large gradients in solutions, which are not well resolved by h or prefinement [1]. The general idea is that the mesh need not conform to the moving boundaries so that minimal or no remeshing is required during the analysis. Our main motivation is to provide a generic implementation of enrichment within a flexible C++ environment, namely the Diffpack platform. The work was inspired by some of our earlier work [6,9] and that of other colleagues [5,7,8]. We demonstrate how object-oriented programming is particularly useful for the treatment of data structures and operations associated with XFEM : mesh-geometry interaction, non-standard integration rules, application of boundary conditions, treatment of level set data [2,6]. We detail the implementation of such features and verify and validate their implementation based on [5]. We show results based on unshifted, shifted [1] and study the behaviour of the stable generalized finite element method (SGFEM) to avoid blending effects and help control the conditioning of the system matrix [4]. For integration of elements cut by interface we use an in-house Delaunay Triangulation algorithm proposed by [3,5] and presented in detail in a companion paper. [less ▲]

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See detailMolecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture
Talebi, H.; Silani, M.; Bordas, Stéphane UL et al

in International Journal for Multiscale Computational Engineering (2013), 11(6), 527-541

We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element ... [more ▼]

We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element method to handle the discontinuities. The coupling is based on the bridging domain method, which blends the continuum and atomistic energies. The Lennard-Jones potential is used to model the interactions in the atomistic domain, and the Cauchy-Born rule is used to compute the material behavior in the continuum domain. To our knowledge, it is the first time that a three dimensional extended bridging domain method is reported. To show the suitability of the proposed method, a threedimensional crack problem with an atomistic region around the crack front is solved. The results show that the method is capable of handling crack propagation and dislocation nucleation. © 2013 by Begell House, Inc. [less ▲]

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See detailDefect engineering of 2D monatomic-layer materials
Peng, Q.; Crean, J.; Dearden, A. K. et al

in Modern Physics Letters B (2013), 27(23),

Atomic-thick monolayer two-dimensional materials present advantageous properties compared to their bulk counterparts. The properties and behavior of these monolayers can be modified by introducing defects ... [more ▼]

Atomic-thick monolayer two-dimensional materials present advantageous properties compared to their bulk counterparts. The properties and behavior of these monolayers can be modified by introducing defects, namely defect engineering. In this paper, we review a group of common two-dimensional crystals, including graphene, graphyne, graphdiyne, graphn-yne, silicene, germanene, hexagonal boron nitride monolayers and MoS2 monolayers, focusing on the effect of the defect engineering on these two-dimensional monolayer materials. Defect engineering leads to the discovery of potentially exotic properties that make the field of two-dimensional crystals fertile for future investigations and emerging technological applications with precisely tailored properties. © World Scientific Publishing Company. [less ▲]

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See detailMesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J. et al

in Computational Mechanics (2013)

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for ... [more ▼]

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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See detailNURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
Valizadeh, N.; Natarajan, S.; Gonzalez-Estrada, O. A. et al

in Composite Structures (2013), 99

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material ... [more ▼]

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates. © 2012 Elsevier Ltd. [less ▲]

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See detailEfficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity
González-Estrada, O. A.; Natarajan, S.; Ródenas, J. J. et al

in Computational Mechanics (2013), 52(1), 37-52

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown ... [more ▼]

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features. © 2012 Springer-Verlag. [less ▲]

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See detailExplicit expressions of dual loads for accurate error estimation and bounding in goal oriented adaptivity
Ródenas, Juan José; Nadal, Enrique; González-Estrada, Octavio Andrés et al

in Moitinho de Almeida, J P; Díez, P; Tiago, C (Eds.) et al Adaptive Modeling and Simulation. Proceedings of VI ADMOS 2013 (2013)

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