References of "Béchet, Eric"
     in
Bookmark and Share    
Full Text
See detailStreamable Laguerre-Voronoi Tessellation Model for Tomographic Images
Leblanc, Christophe ULg; Nguyen, Van Dung ULg; Wan, Fangyi et al

Conference (2014, July 25)

Introduction. Nowadays, the interest in foam materials is growing in several engineering fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen- dent on their ... [more ▼]

Introduction. Nowadays, the interest in foam materials is growing in several engineering fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen- dent on their microstructure [3]. Thus designing foams with specific mechanical properties can be very challenging. The present contribution is part of the ARC-Bridging project [4], whose objective is to predict the mechanical behavior of complex microstructured mate- rials via numerical simulations. A possible classification of foam models into two groups is: random models and deterministic models [5]. The random models frequently require statistical estimations of their parameters [6], whereas the deterministic models generally require numerically expensive image analyse. Indeed, classical analysis steps involve a distance tranform, a watershed and, optionally, a h-minima transform [5, p. 22], which can be computationally demanding [7, 8, 9]. Contribution. In the present Laguerre–Voronoi tessellation model, the image analysis part neither involes the watershed transform, nor the h-minima transform. Instead, fol- lowing the original idea of A.M. Lopez-Reina et E. Béchet [10], these two transforms are respectively replaced by a Hessian-based removal of spurious extrema and a clustering of the remaining maxima. This substitution allows the processing of large 3D-images by slices, i.e. “streaming”. The only limitation is enforced by the distance transform: the “feature” voxel of a given voxel should belong to the same slice. For foam images, this condition is fulfilled as long as the slice’s thickness is larger than the maximal foam cell’s size. Conclusion and perspectives. The aim of this contribution is to provide an efficient tessellation model for tomographic images of foams. From input tomographic images, this model provides a geometry model which will be used as an input for finite element simulations under the ARC-Briding project [4]. Simulation results will be compared with experimental measures. [less ▲]

Detailed reference viewed: 27 (19 ULg)
Full Text
Peer Reviewed
See detailFifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011)
Béchet, Eric ULg; Dick, Erik; Geuzaine, Christophe ULg et al

in International Journal of Computational & Applied Mathematics (2013), 246

Detailed reference viewed: 99 (22 ULg)
Full Text
Peer Reviewed
See detailA Frontal Delaunay Quad Mesh Generator Using the L ∞  Norm
Remacle, J.-F.; Henrotte, F.; Carrier-Baudouin, T. et al

in International Journal for Numerical Methods in Engineering (2013), 94(5), 494-512

Detailed reference viewed: 99 (35 ULg)
Full Text
Peer Reviewed
See detailImposing periodic boundary condition on arbitrary meshes by polynomial interpolation
Nguyen, Van Dung ULg; Béchet, Eric ULg; Geuzaine, Christophe ULg et al

in Computational Materials Science (2012), 55

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with ... [more ▼]

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with appropriate boundary conditions, among which periodic boundary condition is the most efficient in terms of convergence rate. The classical method to impose the periodic boundary condition requires the identical meshes on opposite RVE boundaries. This condition is not always easy to satisfy for arbitrary meshes. This work develops a new method based on polynomial interpolation that avoids the need of matching mesh condition on opposite RVE boundaries. [less ▲]

Detailed reference viewed: 549 (296 ULg)
Full Text
Peer Reviewed
See detailLloyd relaxation using analytical Voronoi diagram in the L_infinite norm and its application to quad optimization
Mouton, Thibaud ULg; Béchet, Eric ULg

in Jiao, Xiangmin (Ed.) Proceedings of the 21st International Meshing Roundtable (2012)

An incremental Delaunay triangulation algorithm to generate Voronoi diagrams within the L∞ norm is presented. The main qualities are the preserva- tion of the simplicity of the classical L2 version and ... [more ▼]

An incremental Delaunay triangulation algorithm to generate Voronoi diagrams within the L∞ norm is presented. The main qualities are the preserva- tion of the simplicity of the classical L2 version and its its intrinsic robustness It is then coupled to the well known Lloyd algorithm for computing Centroidal Voronoi Tesselations of point sets. This algorithm is then used to generate well shaped quadri- lateral meshes. [less ▲]

Detailed reference viewed: 11 (6 ULg)
Full Text
See detailThe extended finite element method for three-dimensional reinforced composites.
Duboeuf, Frédéric ULg; Béchet, Eric ULg

Conference (2011, November 16)

This paper deals with the use of eXtended Finite Element Method (XFEM) to perform local effects in three-dimensional reinforced composites. This method was first introduced to model cracks. It is based on ... [more ▼]

This paper deals with the use of eXtended Finite Element Method (XFEM) to perform local effects in three-dimensional reinforced composites. This method was first introduced to model cracks. It is based on the partition of unity concept and the description of discontinuities like the location of holes and material interfaces is often realized by the level-set method. The approach considered allows (i) to easily model the real geometry of reinforcing fibers (not idealized), (ii) to impose arbitrary Dirichlet and Neumann boundary conditions on the implicit defined boundaries and (iii) to introduce models of degradation. Numerical applications are presented on some academic tests. [less ▲]

Detailed reference viewed: 44 (20 ULg)
Full Text
See detailConversion of a B-Rep CAD model to an implicit representation in the context of the X-FEM
Mouton, Thibaud ULg; Béchet, Eric ULg

Conference (2011, November)

This paper deals with the alternative representation of parametric CAD models in the context of the Extended Finite Element Method (X-FEM) [1]. Partition of unity methods like the X-FEM allows to embed in ... [more ▼]

This paper deals with the alternative representation of parametric CAD models in the context of the Extended Finite Element Method (X-FEM) [1]. Partition of unity methods like the X-FEM allows to embed in finite element functional spaces any discontinuity. It is so theoretically possible to simulate a complete model without any of its geometrical features appearing in the mesh. Nevertheless, X-FEM was at first only used in geometrically simple application (e.g. cracks) due to the lack of method to make features of a complex CAD model to implicitly appear in the functional spaces. The geometry of the crack was originally modeled using Level Sets because of their ability to handle complex surfaces and naturally take into account changes in topology and geometry encountered with moving interfaces. Level Sets modelling has been recently extended in combination with a Constructive Solid Geometry (CSG) approach [2] but this method is still limited by the use of globally defined Level Sets. The proposed algorithm extends the Level Sets modelisation of the geometry using the Boundary Representation (B-Rep) of the object. In this case, Level Sets are only locally defined (Fig a). A sub- mesh is then obtained by cutting a primary fixed mesh (encompassing the CAD model) along with isozero of each Level Set (Fig b). Resulting sub-elements are then sorted to build a temporary topology. One of the difficulties involved is then to match the temporary topology with the original B-Rep topology (Fig c). The aim is to recover unmodified entities and detect deleted or new entities that could appear during the deformation of the object. Finally, examples of computations in linear elasticity will be shown. [less ▲]

Detailed reference viewed: 10 (2 ULg)
See detailProceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011)
Hogge, Michel ULg; Van Keer, Roger; Dick, Erik et al

Book published by Université de Liège - Dépôt légal: D/2011/0480/31 (2011)

Detailed reference viewed: 41 (7 ULg)
Full Text
Peer Reviewed
See detailImposing periodic boundary condition on arbitrary meshes by polynomial interpolation
Nguyen, Van Dung ULg; Béchet, Eric ULg; Geuzaine, Christophe ULg et al

in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November)

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with ... [more ▼]

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with appropriate boundary conditions, among which periodic boundary condition is the most efficient in terms of convergence rate. The classical method to impose the periodic boundary condition requires identical meshes on opposite RVE boundaries. This condition is not always easy to satisfy for arbitrary meshes. This work develops a new method based on polynomial interpolation that avoids the need of the identical mesh condition on opposite RVE boundaries. [less ▲]

Detailed reference viewed: 109 (57 ULg)
Peer Reviewed
See detailA Frontal Delaunay Quad Mesh Generator Using the L ∞  Norm
Remacle, J.-F.; Henrotte, F.; Carrier Baudoin, T. et al

in Proceedings of the 20th International Meshing Roundtable (2011, October)

Detailed reference viewed: 48 (9 ULg)
Full Text
Peer Reviewed
See detailFinite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces
Moumnassi, Mohammed; Belouettar, Salim; Béchet, Eric ULg et al

in Computer Methods in Applied Mechanics & Engineering (2011), 200(5-8), 774-796

In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold ... [more ▼]

In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold: (1) describe and validate a method to represent arbitrary parametric surfaces implicitly; (2) represent arbitrary solids implicitly, including sharp features using level sets and boolean operations; (3) impose arbitrary Dirichlet and Neumann boundary conditions on the resulting implicitly defined boundaries. The methods proposed do not require local refinement of the finite element mesh in regions of high curvature, ensure the independence of the domain’s volume on the mesh, do not rely on boundary regularization, and are well suited to methods based on fixed grids such as the extended finite element method (XFEM). Numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries. This approach is one step in the desired direction of tying numerical simulations to computer aided design (CAD), similarly to the isogeometric analysis paradigm. [less ▲]

Detailed reference viewed: 9 (0 ULg)
Full Text
Peer Reviewed
See detailCalculs de structures basés sur la technique des level sets et la méthode de partition de l'unité
Moumnassi, Mohammed; Béchet, Eric ULg; Belouettar, Salim et al

in Actes du 9ème Colloque National en Calcul des Structures (2009, May)

Detailed reference viewed: 8 (0 ULg)
Full Text
Peer Reviewed
See detailSome numerical experiments about cracked piezoelectric media
Béchet, Eric ULg; Kuna, Meinhard

(2009)

Piezoelectric materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service ... [more ▼]

Piezoelectric materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the extended finite element method (X-FEM) has been applied mostly to model cracks in structural materials. We present convergence results in the energy norm and for the stress intensity factors Then, some results obout inaccuracies in the stresses near the crack tip are presented. [less ▲]

Detailed reference viewed: 18 (2 ULg)
Full Text
Peer Reviewed
See detailApplication of the X-FEM to the fracture of piezoelectric materials
Béchet, Eric ULg; Scherzer, M.; Kuna, M.

in International Journal for Numerical Methods in Engineering (2009), 77(11), 1535-1565

This paper presents an application of the extended finite element method (X-FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New ... [more ▼]

This paper presents an application of the extended finite element method (X-FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the X-FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip Solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright (C) 2008 John Wiley & Sons, Ltd. [less ▲]

Detailed reference viewed: 31 (8 ULg)
Full Text
See detailSimulations in ambient space : freeing mesh generation techniques from the respect of boundaries in the context of the FEM
Béchet, Eric ULg; Moës, Nicolas; Wolhmuth, Barbara et al

Scientific conference (2009)

Numerical simulations made within the finite element method have been made with increased geometrical and modeling complexity over the decades. To carry out such simulations, mesh generation techniques ... [more ▼]

Numerical simulations made within the finite element method have been made with increased geometrical and modeling complexity over the decades. To carry out such simulations, mesh generation techniques are a key ingredient. With conventional finite element methods, one first need to conform the mesh to the boundaries. The density of the mesh should also be controlled. Altogether, these require tough mesh generation algorithms and often a fair amount of user interaction. In this paper, we present a technique that allows to free mesh generation algorithms from the respect of object boundaries or internal boundaries. First we will show a way to represent the geometry of an object independently of its origin, using multiple level-sets. We will then show how to embed those interfaces in the finite element method without having to conform the mesh. We prove that the numerical results are as accurate as those obtained with conforming boundaries. [less ▲]

Detailed reference viewed: 90 (13 ULg)
Full Text
Peer Reviewed
See detailA stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
Béchet, Eric ULg; Moes, Nicolas; Wohlmuth, Barbara

in International Journal for Numerical Methods in Engineering (2009), 78(8), 931-954

This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier ... [more ▼]

This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier approaches. we do not work with an interior penalty formulation as, e.g. for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. Roughly speaking a stable and optimal discrete Lagrange multiplier space has to satisfy two criteria: a best approximation property and a uniform inf-sup condition. Owing to the fact that the interface does not match the edges of the mesh, the choice of a good discrete Lagrange Multiplier space is not trivial. Here we propose a new algorithm for the local construction of the Lagrange Multiplier space and show that a uniform inf-sup condition is satisfied. A counterexample is also presented, i.e. the inf-sup constant depends on the mesh-size and degenerates as it tends to zero. Numerical results in two-dimensional confirm the theoretical ones. Copyright (C) 2008 John Wiley & Sons, Ltd. [less ▲]

Detailed reference viewed: 125 (7 ULg)
Full Text
Peer Reviewed
See detailDesign of a Stable Lagrange Multiplier Space for Stiff Boundary Conditions
Béchet, Eric ULg; Moës, Nicolas; Wohlmuth, Barbara

in Zilian, A.; Fries, T. P. (Eds.) International Conference on Extended Finite Element Methods – Recent Developments and Applications XFEM 2009 (2009)

We introduce a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the eXtended Finite Element Method. In contrast to earlier approaches ... [more ▼]

We introduce a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the eXtended Finite Element Method. In contrast to earlier approaches, we do not work with an interior penalty formulation as, e.g., for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. The new algorithm allows a local construction of the Lagrange multiplier space while improving the accuracy of the computed fields. The originality of this approach with regard to former approaches lies in the use of the trace of primary shape functions defined on the domain, and a simplified procedure to define the mesh on the interface. Moreover, the newly constructed Lagrange multiplier space satisfies, in contrast to the naive approach, a uniform inf-sup condition. [less ▲]

Detailed reference viewed: 80 (19 ULg)
See detailDesign of a stable LM space for stiff boundary conditions and interfacial constraints
Béchet, Eric ULg

Scientific conference (2008, October)

Detailed reference viewed: 6 (0 ULg)
See detailRecent developpments of the X-FEM applied to piezoelectric fracture mechanics
Béchet, Eric ULg

Scientific conference (2008, January)

Detailed reference viewed: 13 (1 ULg)
Full Text
Peer Reviewed
See detailX-FEM explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries
Rozycki, P.; Moes, N.; Béchet, Eric ULg et al

in Computer Methods in Applied Mechanics & Engineering (2008), 197(5), 349-363

This paper deals with the use of the extended Finite Element Method (X-FEM) for rapid dynamic problems. To solve the equations of motion, a common technique is the explicit direct integration with a ... [more ▼]

This paper deals with the use of the extended Finite Element Method (X-FEM) for rapid dynamic problems. To solve the equations of motion, a common technique is the explicit direct integration with a Newmark scheme. Since this temporal scheme is only conditionally stable, the critical time step must be determined. It is generally induced by mesh constraints. The idea of the paper is to weaken constraints on mesh generation algorithms so that the critical time step is as large as possible. Using the X-FEM one allows a non-conformity between mesh and discontinuities such as cracks, holes or interfaces. In a first part, we present a summary about direct integration schemes and about the eXtended Finite Element Method. Then, we focus on the theoretical description of a ID X-FEM finite element and its generalization to 2D and 3D finite elements. Then, dynamic numerical simulations are shown. They concern structures under impact with holes or external boundaries not exactly matched by the mesh. Comparisons are made with numerical results coming from the ABAQUS software. It shows that developments are satisfactory. We conclude with some outlooks concerning this work. (c) 2007 Elsevier B.V. All rights reserved. [less ▲]

Detailed reference viewed: 79 (5 ULg)