References of "Bordas, Stéphane 50000969"
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See detailCertification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error
Kerfriden, Pierre; Ródenas, Juan-José; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2014), 97(6), 395-422

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction ... [more ▼]

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the nite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model. [less ▲]

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See detailMeshless Elasticity Model and Contact Mechanics-based Verification Technique
Aras, Rifat; Shen, Yuzhong; Audette, Michel et al

in MICCAI Computational Biomechanics for Medicine (2014, January 01)

Mesh-based techniques are well studied and established methods for solving continuum biomechanics problems. When the problem at hand involves extreme deformations or artificial discontinuities, meshless ... [more ▼]

Mesh-based techniques are well studied and established methods for solving continuum biomechanics problems. When the problem at hand involves extreme deformations or artificial discontinuities, meshless methods provide sev-eral advantages over the mesh-based methods. This work discusses the Moving Least Square approximation-based meshless collocation method for simulating de-formable objects and presents a verification technique that is based on the Hertzian theory of non-adhesive elastic contact. The effectiveness of the Hertzian contact theory as a means for verification was first tested and proven through a well-established FEM code, FEBio. The meshless method was implemented as a reusable component for the SOFA framework, an open source software library for real-time simulations. Through experimentation, the Hertzian theory has been tested against SOFA hexahedral FEM and the meshless models within the SOFA framework. Convergence studies and L2 error curves are provided for both mod-els. Experimental results demonstrated the effectiveness of the implementation of the meshless method. [less ▲]

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See detailA Two-Dimensional Isogeometric Boundary Element Method For Linear Elastic Fracture
Peng, Xuan; AtroShchenko, Elena; Simpson, Robert et al

Scientific Conference (2014, January)

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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 detailGradient Smoothing for Nearly Incompressible Hyperealsticity
Lee, Chang-Kye; Mihai, L. Angela; Kerfriden, Pierre et al

Poster (2014)

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See detailGradient Smoothing for Nearly Incompressible Hyperelasticity
Lee, Chang-Kye; Mihai, L. Angela; Kerfriden, Pierre et al

Poster (2014)

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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 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 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 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 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 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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See detailEfficient modeling of random heterogeneous materials with an uniform probability density function (slides)
Paladim, Daniel; Kerfriden, Pierre; Moitinho de Almeida, José et al

Scientific Conference (2014)

Homogenised constitutive laws are largely used to predict the behaviour of composite structures. Assessing the validity of such homogenised models can be done by making use of the concept of “modelling ... [more ▼]

Homogenised constitutive laws are largely used to predict the behaviour of composite structures. Assessing the validity of such homogenised models can be done by making use of the concept of “modelling error”. First, a microscopic “faithful” -and potentially intractable- model of the structure is defined. Then, one tries to quantify the effect of the homogenisation procedure on a result that would be obtained by directly using the “faithful” model. Such an approach requires (a) the “faithful” model to be more representative of the physical phenomena of interest than the homogenised model and (b) a reliable approximation of the result obtained using the ”faithful” and intractable model to be available at cheap costs. We focus here on point (b), and more precisely on the extension of the techniques devel- oped in [3] [2] to estimate the error due to the homogenisation of linear, spatially random composite materials. Particularly, we will approximate the unknown probability density function by bounding its first moment. In this paper, we will present this idea in more detail, displaying the numerical efficiencies and computational costs related to the error estimation. The fact that the probability density function is uniform is exploited to greatly reduce the computational cost. We will also show some first attempts to correct the homogenised model using non-conforming, weakly intrusive microscopic patches. [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 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 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 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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