References of "Bordas, Stéphane 50000969"
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See detailQuasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
Beex, Lars UL; Kerfriden, Pierre; Rabczuk, Timon et al

in Computer Methods in Applied Mechanics and Engineering (2014), 279

The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a ... [more ▼]

The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice. [less ▲]

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See detailAn extended finite element method (XFEM) for linear elastic fracture with smooth nodal stress
Peng, Xuan; Kulasegaram, Sivakumar; Bordas, Stéphane UL et al

in Engineering Fracture Mechanics (2014)

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See detailAn efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL et al

in Numerical Methods for Partial Differential Equations (2014)

In this paper, we study the class of linear elastodynamic problems with a ne parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main ... [more ▼]

In this paper, we study the class of linear elastodynamic problems with a ne 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 strategy within the RB approximation context. The proposed sampling strategy looks for the parameter points such that the output error approximation will be minimized by Greedy iterations. In estimating such output error approximation, the standard POD-Greedy algorithm is invoked to provide enriched RB approximations for the FE outputs. We propose a so-called "cross-validation" process to choose adaptively the dimension of the enriched RB space corresponding with the dimension of the RB space under consideration. Numerical results show that the new goal-oriented POD-Greedy sampling procedure with the cross-validation process improves signi ficantly the space-time output computations in comparison with the ones computed by the standard POD-Greedy algorithm. The method is thus ideally suited for repeated, rapid and reliable evaluations of input-output relationships in the space-time setting. [less ▲]

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See detailStochastic modelling of clay/epoxy nanocomposites
Silani, Mohammad; Talebi, Hossein; Ziaei-Rad, Saeed et al

in Composite Structures (2014), 118

This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and ... [more ▼]

This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and matrix is taken into account by introducing an appropriate stochastic damage modelling at the nano scale. Then, the overall properties of the nanocomposite are upscaled using computational homogenisation. Two mechanical properties are investigated: the random distribution of the homogenised Young’s modulus and the overall loss of stiffness observed in the case of extreme loading. The results obtained in the former case are in good agreement with experimental results from the literature. In the second case, we show that exfoliation does not significantly affect the overall strength of the nanocomposite. [less ▲]

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See detailExplicit finite deformation analysis of isogeometric membranes
Chen, Lei; Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung et al

in Computer Methods in Applied Mechanics and Engineering (2014)

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear ... [more ▼]

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear kinematics employs the Kirchhoff-Love shell theory to describe the mechanical behaviour of thin to ultrathin structures. The displacement fields are interpolated from the displacements of control points only, and no rotational degrees of freedom are used at control points. Due to the high order Ck (k ≥ 1) continuity of NURBS shape functions the Kirchhoff-Love theory can be seamlessly implemented. An explicit time integration scheme is used to compute the transient response of membrane structures to time-domain excitations, and a dynamic relaxation method is employed to obtain steady-state solutions. The versatility and good performance of the present formulation is demonstrated with the aid of a number of test cases, including a square membrane strip under static pressure, the inflation of a spherical shell under internal pressure, the inflation of a square airbag and the inflation of a rubber balloon. The mechanical contribution of the bending stiffness is also evaluated. [less ▲]

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See detailAn integrated design-analysis framework for three dimensional composite panels
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL et al

in Computer-Aided Design (2014)

We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the ... [more ▼]

We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the isogeometric concept recently emerged in the computational mechanics community. Using the presented approach, finite element analysis of composite panels can be performed with the only input is the geometry representation of the composite surface. In this paper, non-uniform rational B-splines (NURBS) are used to represent the panel surfaces. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. [less ▲]

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See detailPOD-based model order reduction for the simulation of strong nonlinear evolutions in structures: Application to damage propagation
Kerfriden, P.; Gosselet, P.; Adhikari, S. et al

in IOP Conference Series: Materials Science and Engineering (2014), 10(1),

In this paper, we develop a bridge between POD-based model order reduction techniques and the classical Newton-Krylov solvers to derive an efficient solution procedure for highly nonlinear problems ... [more ▼]

In this paper, we develop a bridge between POD-based model order reduction techniques and the classical Newton-Krylov solvers to derive an efficient solution procedure for highly nonlinear problems undergoing strong topological changes. [less ▲]

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See detailBoundary Element Method with NURBS-geometry and independent field approximations in plane elasticity
Atroshchenko, Elena; Peng, Xuan; Hale, Jack et al

Scientific Conference (2014)

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See detailIsogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL et al

in Computer-Aided Design (2014), 55

Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset ... [more ▼]

Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset algorithm. The proposed offset algorithm, which is required by IGA, is non-existent in the CAD literature. Using the presented approach, finite element analysis of composite panels can be performed with the only input being the geometry representation of the composite surface. The method proposed provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. Different parts (patches) can be parametrized independently of each other and glued together, in the finite element solver, by a discontinuous Galerkin method. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. © 2014 Elsevier Ltd. All rights reserved. [less ▲]

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See detailOn the equivalence between the cell-based smoothed finite element method and the virtual element method
Natarajan, Sundararajan; Bordas, Stéphane UL; Ean Tat, Ooi

E-print/Working paper (2014)

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity ... [more ▼]

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEMis combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D. [less ▲]

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See detailIsogeometric finite element analysis using polynomial splines over hierarchical T-meshes
Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung; Bordas, Stéphane UL et al

in IOP Conference Series: Materials Science and Engineering (2014), 10(1),

Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric ... [more ▼]

Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples. [less ▲]

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See detailIsogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory
Thai, C. H. A; Bordas, Stéphane UL; Ferreira, A. et al

in European Journal of Mechanics. A, Solids (2014), 43

This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear ... [more ▼]

This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear stresses are vanished at the top and bottom surfaces of the plates and shear correction factors are no longer required. A weak form of the static, free vibration and buckling models for laminated composite and sandwich plates based on ITSDT is then derived and is numerically solved using an isogeometric analysis (IGA). The proposed formulation requires C1-continuity generalized displacements and hence basis functions used in IGA fulfill this requirement. Numerical examples are provided to show high efficiency of the present method compared with other published solutions. © 2013 Elsevier Ltd. All rights reserved. [less ▲]

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See detailNitsche’s method for two and three dimensional NURBS patch coupling
Nguyen, VP; Kerfriden, Pierre; Brino, Marco et al

in Computational Mechanics (2014), 53(6), 1163-1182

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear ... [more ▼]

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications. [less ▲]

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See detailDamage tolerance assessment directly from CAD: (extended) isogeometric boundary element methods (XIGABEM)
Peng, Xuan; Atroshchenko, Elena; Bordas, Stéphane UL

Scientific Conference (2014)

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See detailAnalysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method
Natarajan, S; Ferreira; Bordas, Stéphane UL et al

in Mathematical Problems in Engineering (2014), Article ID 247932

In this paper, a cell based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, mechanical and thermal buckling behaviour of ... [more ▼]

In this paper, a cell based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first order shear deformation theory and the shear locking is suppressed by a discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence the gradient index, the plate aspect ratio, skewness of the plate and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied. [less ▲]

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See detailAnalysis using higher-order XFEM: implicit representation of geometrical features from a given parametric representation
Moumnassi, Mohammed; Bordas, Stéphane UL; Figueredo, R et al

in Mechanics and Industry (2014), 15(05), 443-448

We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong ... [more ▼]

We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach. [less ▲]

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See detailAnalysis of composite plates through cell-based smoothed finite element and 4-noded mixed interpolation of tensorial components techniques
Rodrigues, J. D.; Natarajan, S.; Ferreira, Ana UL et al

in Computers and Structures (2014), 135

The static bending and the free vibration analysis of composite plates are performed with Carrera's Unified Formulation (CUF). We combine the cell-based smoothed finite element method (CSFEM) and the 4 ... [more ▼]

The static bending and the free vibration analysis of composite plates are performed with Carrera's Unified Formulation (CUF). We combine the cell-based smoothed finite element method (CSFEM) and the 4-noded mixed interpolation of tensorial components approach (MITC4). The smoothing method is used for the approximation of the bending strains, whilst the mixed interpolation allows the calculation of the shear transverse stress in a different manner. With a few numerical examples, the accuracy and the efficiency of the approach is demonstrated. The insensitiveness to shear locking is also demonstrated. © 2014 Elsevier Ltd. All rights reserved. [less ▲]

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See detailAn experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae
Cahill, L. M. A.; Natarajan, S.; Bordas, Stéphane UL et al

in Composite Structures (2014), 107

This paper presents an enriched finite element method to simulate the growth of cracks in linear elastic, aerospace composite materials. The model and its discretisation are also validated through a ... [more ▼]

This paper presents an enriched finite element method to simulate the growth of cracks in linear elastic, aerospace composite materials. The model and its discretisation are also validated through a complete experimental test series. Stress intensity factors are calculated by means of an interaction integral. To enable this, we propose application of (1) a modified approach to the standard interaction integral for heterogeneous orthotropic materials where material interfaces are present; (2) a modified maximum hoop stress criterion is proposed for obtaining the crack propagation direction at each step, and we show that the “standard” maximum hoop stress criterion which had been frequently used to date in literature, is unable to reproduce experimental results. The influence of crack description, material orientation along with the presence of holes and multi-material structures are investigated. It is found, for aerospace composite materials with View the MathML source ratios of approximately 10, that the material orientation is the driving factor in crack propagation. This is found even for specimens with a material orientation of 90°, which were previously found to cause difficulty in both damage mechanics and discrete crack models e.g. by the extended finite element method (XFEM). The results also show the crack will predominantly propagate along the fibre direction, regardless of the specimen geometry, loading conditions or presence of voids. [less ▲]

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See detailTwo- and three-dimensional isogeometric cohesive elements for composite delamination analysis
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL

in Composites. Part B, Engineering (2014), 60

We propose an automatic numerical method requiring minimal user intervention to simulate delamination in composite structures. We develop isogeometric cohesive elements for two- and three-dimensional ... [more ▼]

We propose an automatic numerical method requiring minimal user intervention to simulate delamination in composite structures. We develop isogeometric cohesive elements for two- and three-dimensional delamination by exploiting the knot insertion algorithm directly from CAD data to generate cohesive elements along delamination. A complete computational framework is presented including pre-processing, processing and post-processing. They are explained in detail and implemented in MIGFEM - an open source Matlab Isogemetric Analysis code developed by the authors. The composite laminates are modeled using both NURBS solid and rotation-free shell elements. Several two and three dimensional examples ranging from standard delamination tests (the mixed mode bending test) to the L-shaped specimen with a fillet, three dimensional (3D) double cantilever beam and a 3D singly curved thick-walled laminate are provided. The method proposed provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. © 2013 Elsevier Ltd. All rights reserved. [less ▲]

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See detailReal-time simulation of contact and cutting of heterogeneous soft-tissues
Courtecuisse, H.; Allard, J.; Kerfriden, P. et al

in Medical Image Analysis (2014), 18(2), 394-410

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and ... [more ▼]

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and other topological changes. We provide an integrated methodology able to deal both with the ill-conditioning issues associated with material heterogeneities, contact boundary conditions which are one of the main sources of inaccuracies, and cutting which is one of the most challenging issues in interactive simulations. Our approach is based on an implicit time integration of a non-linear finite element model. To enable real-time computations, we propose a new preconditioning technique, based on an asynchronous update at low frequency. The preconditioner is not only used to improve the computation of the deformation of the tissues, but also to simulate the contact response of homogeneous and heterogeneous bodies with the same accuracy. We also address the problem of cutting the heterogeneous structures and propose a method to update the preconditioner according to the topological modifications. Finally, we apply our approach to three challenging demonstrators: (i) a simulation of cataract surgery (ii) a simulation of laparoscopic hepatectomy (iii) a brain tumor surgery. © 2013 Elsevier B.V. [less ▲]

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