References of "Béchet, Eric"
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See detailIon Mobility-Mass Spectrometry: Going beyond the numbers
Haler, Jean ULg; Far, Johann ULg; Béchet, Eric ULg et al

Scientific conference (2017, July 03)

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See detailFinite element model reduction for space thermal analysis
Jacques, Lionel ULg; Béchet, Eric ULg; Kerschen, Gaëtan ULg

in Finite Elements in Analysis and Design (2017), 127

To alleviate the computational burden of the nite element method for thermal analyses involving conduction and radiation, this paper proposes an automatic conductive-radiative reduction process based on ... [more ▼]

To alleviate the computational burden of the nite element method for thermal analyses involving conduction and radiation, this paper proposes an automatic conductive-radiative reduction process based on the clustering of a detailed mesh coming from a structural model for instance. The proposed method leads to a signi cant reduction of the number of radiative exchange factors (REFs) to compute and size of the corresponding matrix. It further keeps accurate conduction information by introducing the concept of physically meaningful super nodes. The REFs between the super nodes are computed through Monte Carlo ray-tracing on the partitioned mesh, preserving the versatility of the method. The resulting conductive-radiative reduced model is solved using standard iterative techniques and the detailed mesh temperatures can be recovered from the super nodes temperatures for further thermo-mechanical analysis. The proposed method is applied to a structural component of the Meteosat Third Generation mission and is benchmarked against ESATAN-TMS, the standard thermal analysis software used in the European aerospace industry. [less ▲]

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See detailEmbedded solids of any dimension in the X-FEM. Part I - Building a dedicated P1 function space
Duboeuf, Frédéric ULg; Béchet, Eric ULg

in Finite Elements in Analysis and Design (2017)

This paper focuses on the design of a dedicated P1 function space to model elliptic boundary value problem on a manifold embedded in a space of higher dimension. Using the traces of the linear P1 shape ... [more ▼]

This paper focuses on the design of a dedicated P1 function space to model elliptic boundary value problem on a manifold embedded in a space of higher dimension. Using the traces of the linear P1 shape functions, it introduces an algorithm to reduce the function space into an equivalent space having the same properties than a P1 Lagrange approximation. Convergence studies involving problems of codimension one or two embedded in 2D or 3D show good accuracy with regard to classical finite element and analytical solutions. The effects of the relative position of the domain with respect to the mesh are studied in a sensitivity analysis; it illustrates how the proposed solution allows to keep the condition number bounded. A comparative study is performed with the method introduced by Olshanskii et al. 2009 on a closed surface to validate our approach. The robustness of the proposed approach is investigated with regard to their method and that of Burman et al. 2016. This paper is the first in a series of two, on the topic of embedded solids of any dimension within the context of the extended finite element method. It investigates problems involving borderless domains or domains with boundary subject to Dirichlet constraint defined only on the boundaries of the bulk mesh, while the forthcoming paper overcomes this limitation by introducing a new stable Lagrange multiplier space for Dirichlet boundary condition (and more generally stiff condition), that is valid for every combination of the background mesh and manifold dimensions. The combination of both algorithms allows to handle any embedding i.e. 1D, 2D and 3D problems embedded in 2D or 3D background meshes. [less ▲]

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See detailEmbedded solids of any dimension in the X-FEM. Part II - Imposing Dirichlet boundary conditions
Duboeuf, Frédéric ULg; Béchet, Eric ULg

in Finite Elements in Analysis and Design (2017)

This paper focuses on the design of a stable Lagrange multiplier space dedicated to enforce Dirichlet boundary conditions on embedded boundaries of any dimension. It follows a previous paper in a series ... [more ▼]

This paper focuses on the design of a stable Lagrange multiplier space dedicated to enforce Dirichlet boundary conditions on embedded boundaries of any dimension. It follows a previous paper in a series of two, on the topic of embedded solids of any dimension within the context of the extended finite element method. While the first paper is devoted to the design of a dedicated P1 function space to solve elliptic equations defined on manifolds of codimension one or two (curves in 2D and surfaces in 3D, or curves in 3D), the general treatment of Dirichlet boundary conditions, in such a setting, remains to be addressed. This is the aim of this second paper. A new algorithm is introduced to build a stable Lagrange multiplier space from the traces of the shape functions defined on the background mesh. It is general enough to cover: (i) boundary value problems investigated in the first paper (with, for instance, Dirichlet boundary conditions defined along a line in a 3D mismatching mesh); but also (ii) those posed on manifolds of codimension zero (a domain embedded in a mesh of the same dimension) and already considered in Béchet et al. 2009. In both cases, the compatibility between the Lagrange multiplier space and that of the bulk approximation (the dedicated P1 function space used in (i), or classical shape functions used in (ii)) — resulting in the inf–sup condition — is investigate through the numerical Chapelle-Bath test. Numerical validations are performed against analytical and finite element solutions on problems involving 1D or 2D boundaries embedded in a 2D or 3D background mesh. Comparisons with Nitsche’s method and the stable Lagrange multiplier space proposed in Hautefeuille et al. 2012, when they are feasible, highlight good performance of the approach. [less ▲]

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See detailSemi-implicit representation of sharp features with level sets
Asadi Kalameh, Hossein ULg; Pierard, Olivier; Friebel, Christophe et al

in Finite Elements in Analysis and Design (2016), 117-118

The present contribution enriches the nowadays “classical” level set implicit representation of geometries with topological information in order to correctly represent sharp features. For this, sharp ... [more ▼]

The present contribution enriches the nowadays “classical” level set implicit representation of geometries with topological information in order to correctly represent sharp features. For this, sharp features are classified according to their positions within elements of the level set support. Based on this additional information, sub-elements and interface-mesh used in a finite element context for integration and application of boundary conditions are modified to match exactly to the sharp features. In order to analyze evolving geometries, Boolean operations on these semi-implicit representations are derived so that the minimal additional information to represent correctly the new geometry is stored. This approach has been successfully applied to complex two-dimensional geometries. It computes in a robust way numerous Boolean operations and guarantees the precision and the convergence rate of the numerical simulations. [less ▲]

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See detailEmbedded solids of any dimension in the X-FEM defined on higher-order approximations
Duboeuf, Frédéric ULg; Béchet, Eric ULg

Conference (2016, June 06)

Embedded interface methods bring a significant simplification of the modelling process before analysis. Complex geometries and moving boundaries may be described with great flexibility, reducing the ... [more ▼]

Embedded interface methods bring a significant simplification of the modelling process before analysis. Complex geometries and moving boundaries may be described with great flexibility, reducing the meshing step to that of a simple bounding box. Following this idea – to dissociate the field approximation from the geometric description – manifolds of different dimensions may be embedded in the same bulk mesh. However, special attention should be given to the difference of dimensions between that of problem domain and that of bulk mesh (the codimension). Whereas the direct use of the shape functions of the bulk mesh is possible for a problem domain of codimension zero, this approach is no longer possible in other configurations, for instance a beam in a 3D mesh. Unlike approaches introducing independent overlapping meshes for each subdomain, function spaces may be built from the traces of higher dimensional spaces built upon the bulk mesh. For closed curves in 2D and closed surfaces in 3D, the resulting discrete method based on P1 FE have already been studied in the literature. To avoid badly conditioned linear systems, specific treatments are required, e.g. preconditioning approaches or stabilization techniques. Here, we propose to deplete wisely the trace space. We investigate higher-order function spaces to solve the diffusion equation in embedded solids of any codimension. A new space-reducer algorithm is introduced to design the dedicated spaces that avoids ill-conditionning while treating boundary conditions. We present the results of several numerical experiments with convergence analyses. To conclude, applications of this technique to embedded beams or shells is discussed. [less ▲]

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See detailSimulation of contact on crack lips and its influence on fatigue life prediction
Pierard, Olivier; Jin, Yuan; Wyart, Eric et al

Conference (2016, June 01)

his work is dedicated to evaluate the influence of the contact on crack lips on crack path and crack growth rate under multi-axial loading conditions. An important part is dedicated to algorithmic ... [more ▼]

his work is dedicated to evaluate the influence of the contact on crack lips on crack path and crack growth rate under multi-axial loading conditions. An important part is dedicated to algorithmic robustness when handling contact in the context of XFEM in presence of crack tip enrichment functions. Crack path predictions as well as crack growth rate are also strongly influenced by the partial contact so that expressions classically used in the context of uniaxial loading without contact must be adapted. Preliminary simulations of a cracked cylinder submitted to four points bending under multiaxial loading conditions are presented and will be compared to experimental results. [less ▲]

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See detailCrack Lip Contact Modeling Based on Lagrangian Multipliers with X-FEM
Jin, Yuan; Pierard, Olivier; Wyard, Eric et al

in Benvenuti, Elena; Ventura, Guilio (Eds.) Advances in Discretization Methods (2016)

The eXtended Finite Element Method (X-FEM), developed intensively in the past 15 years has become a competitive tool for the solution of problems with evolving discontinuities and singul arities. In the ... [more ▼]

The eXtended Finite Element Method (X-FEM), developed intensively in the past 15 years has become a competitive tool for the solution of problems with evolving discontinuities and singul arities. In the present study, we focus on the application of X-FEM on frictionless contact problems in the context of fracture mechanics. A promising approach in the literature counting for this problem consists in applying Lagrangian multipliers. Meanwhile, as pointed out in Ji and Dolbow (Int J Numer Methods Eng 61:2508–2535, 2004), a naive choice for Lagrangian multiplier space leads to oscillatory multipliers on the contact surface. This oscillation results from a non-uniform but mesh-dependent inf-sup condition. In this work, we adapt the algorithm proposed in Béchet et al. (Int J Numer Methods Eng 78:931–954, 2009) on crack lip contact by di scretizing the displacement field with both scalar and vector tip enrichment functions (Chevaugeon et al., Int J Multiscale Comput Eng 11: 597–631, 2013). The influence of the tip enrichment functions on the stability of the formulation is addressed. We show evidences that the vector enrichment functions can improve the conditioning of the problem without jeopardizing the simulation accuracy in the presence of contact. [less ▲]

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See detailExperimental and computational micro–mechanical investigations of compressive properties of polypropylene/multi–walled carbon nanotubes nanocomposite foams
Wan, Fangyi; Tran, Minh Phuong; Leblanc, Christophe ULg et al

in Mechanics of Materials (2015), 91(Part 1), 95-118

The compressive behavior of nanocomposite foams is studied by both experimental and computational micro-mechanics approaches with the aim of providing an efficient computational model for this kind of ... [more ▼]

The compressive behavior of nanocomposite foams is studied by both experimental and computational micro-mechanics approaches with the aim of providing an efficient computational model for this kind of material. The nanocomposites based on polypropylene (PP) and different contents of multi-walled carbon nanotubes (CNTs) are prepared by melt mixing method. The nanocomposite samples are foamed using super-critical carbon dioxide (ScCO2) as blowing agent at different soaking temperatures. The influence of this foaming parameter on the morphological characteristics of the foam micro-structure is discussed. Differential Scanning Calorimetry (DSC) measurements are used to quantify the crystallinity degree of both nanocomposites and foams showing that the crystallinity degree is reduced after the foaming process. This modification leads to mechanical properties of the foam cell walls that are different from the raw nanocomposite PP/CNTs material. Three--point bending tests are performed on the latter to measure the flexural modulus in terms of the crystallinity degree. Uniaxial compression tests are then performed on the foamed samples under quasi-static conditions in order to extract the macro-scale compressive response. Next, a two-level multi-scale approach is developed to model the behavior of the foamed nanocomposite material. On the one hand, the micro-mechanical properties of nanocomposite PP/CNTs cell walls are evaluated from a theoretical homogenization model accounting for the micro-structure of the semi-crystalline PP, for the degree of crystallinity, and for the CNT volume fraction. The applicability of this theoretical model is demonstrated via the comparison with experimental data from the described experimental measurements and from literature. On the other hand, the macroscopic behavior of the foamed material is evaluated using a computational micro-mechanics model using tetrakaidecahedron unit cells and periodic boundary conditions to estimate the homogenized properties. The unit cell is combined with several geometrical imperfections in order to capture the elastic collapse of the foamed material. The numerical results are compared to the experimental measurements and it is shown that the proposed unit cell computational micro-mechanics model can be used to estimate the homogenized behavior, including the linear and plateau regimes, of nanocomposite foams. [less ▲]

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See detailNumerical simulations on embedded solids : integration of CAD and eXtended Finite Element Analysis
Duboeuf, Frédéric ULg; Béchet, Eric ULg

Conference (2015, September 10)

The aim of this communication is to propose a procedure in order to dissociate the geometric description of the field’s approximation within the extended finite element method (X-FEM) and with non ... [more ▼]

The aim of this communication is to propose a procedure in order to dissociate the geometric description of the field’s approximation within the extended finite element method (X-FEM) and with non-matching meshes. Implicit and explicit approaches are combined in order to represent with accuracy all the CAD entities regardless of their dimension. The choice of appropriate tools such as Level Sets technique allows to describe evolving interfaces with great flexibility. The design of a dedicated P1 functional space is achieved by decimating the traces of standard finite element (FE) shape functions, thanks to a new algorithm, especially when the problem domain is embedded in a space of a higher dimension. An analysis of the approximation properties of the P1 FE trace spaces on hyper-surfaces is available in the literature and applied for solving PDEs on closed surfaces without boundary. Dirichlet boundary conditions are applied using a convenient choice of stable Lagrange multiplier space, according to a new generalized algorithm. That extends the existing solutions to every combination of the space domain and boundary dimensions. In terms of solvers, the introduction of double Lagrange multipliers can be used to recover the positive definiteness of the bilinear form. This approach allows to treat any embedding, i.e. 1, 2, or 3D problems embedded in 2 or 3D background meshes. The possibility of applying the methodology to beams is investigated, with a potential application to through-thickness reinforced composites in a mixed-dimensional modelling framework. [less ▲]

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See detailExact Representation of Interfaces Using Enriched Level-Set Technique
Asadi Kalameh, Hossein ULg; Pierard, Olivier; Béchet, Eric ULg

Conference (2015, July)

This work aims to improve implicit representation of complex industrial work-pieces by reducing the existing gap between Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The proposed ... [more ▼]

This work aims to improve implicit representation of complex industrial work-pieces by reducing the existing gap between Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The proposed approach is based on the level-set technique [1]. Limitations of the latter technique results in the miss-capturing of corners lying on the interface (iso-0 level-set) and other sharp features. These limitations also have a significant impact on surrounding elements. In order to avoid undesired over-smoothing to the sharp features, especially corners, an enhanced representation is proposed that is based on level sets method is introduced. This technique, referred in what follows by “level-set+” ,enriches the classical level-set by using data related to the corner points. This is done by automatically detecting geometrical points and using this information in the implicit representation. Elements containing these geometrical points and surrounding elements will be re-subdivided according to the updated iso-contour. This technique helps to employ classical level set and preserve current data structure for most of the creation of the iso-0 level set. Although the method is general enough to handle most possible configurations in terms of the corner locations, there are still limitations which have been handled in such a way to prevent computational failure. Also, the technique is effective at reducing the memory requirements by automatically erasing sharp features that are no longer existing after e.g. boolean operations. Some novel results illustrates accurate implicit representations of boundaries including the exact capture of sharp features in 2D and 3D. All the developments are implemented in our in-house finite element software Morfeo. There are numerous applications which can benefit from the above mentioned developments including crack propagation with the X-FEM method and transient machining simulations. [less ▲]

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See detailSimulations numériques sur des solides plongés, dans un contexte X-FEM
Duboeuf, Frédéric ULg; Béchet, Eric ULg

in Actes du 11ème colloque national en calcul des structures (2015, May 20)

Ce travail traite des différents enjeux pour conserver toutes les capacités des calculs par éléments finis, en s’affranchissant des maillages conformes à la géométrie. La représentation de la géométrie ... [more ▼]

Ce travail traite des différents enjeux pour conserver toutes les capacités des calculs par éléments finis, en s’affranchissant des maillages conformes à la géométrie. La représentation de la géométrie, la construction d’un espace fonctionnel adapté et l’imposition des conditions aux limites sont abordées dans le contexte de la méthode des éléments finis étendus, tout particulièrement en présence de solides plongés dans un espace de dimension supérieure. L’approche proposée permet de traiter tout type de plongement, c.-à-d. des problèmes 1, 2, et/ou 3D plongés dans des maillages 2 ou 3D. [less ▲]

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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 ▲]

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See detailEmbedded solids of any dimensions in the extended finite element method
Duboeuf, Frédéric ULg; Béchet, Eric ULg

Conference (2014, July 23)

First, we propose a new methodology to enforce Dirichlet boundary conditions in the X-FEM, available for every combination of the space and boundary dimensions. Second, we introduce a new algorithm to ... [more ▼]

First, we propose a new methodology to enforce Dirichlet boundary conditions in the X-FEM, available for every combination of the space and boundary dimensions. Second, we introduce a new algorithm to define a reduced function space over an embedded solid of arbitrary dimension. The combination of both algorithms allows to treat any embedding i.e. 1, 2 and 3D problems embedded in 2 or 3D background meshes. [less ▲]

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See detailIMPLICIT REPRESENTATION OF BOUNDARIES USING LEVEL-SETS FOR TRANSIENT MACHINING APPLICATION
Asadi Kalameh, Hossein ULg; Pierard, Olivier; Béchet, Eric ULg

Conference (2014, July)

This work aims at improving implicit representation of complex industrial work-pieces by reducing the existing gap between Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The proposed ... [more ▼]

This work aims at improving implicit representation of complex industrial work-pieces by reducing the existing gap between Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The proposed approach is based on the level-set technique [1]. Some novel results for accurate implicit representation of boundary include exact capture of sharp features as well as suitable approximation of curved boundaries for nite element computations [2]. This is done by detecting automatically geometrical points of the geometry and use this information in the implicit representation. Then, a Sweep Line Algorithm is used to subdivide the elements containing these geometrical points [3]. The method is general enough in order to describe automatically any arbitrary surface. All the developments are implemented in the commercial nite element package Mor- feo. Numerous applications can bene t from these developments including Cartesian grid problems as well as crack propagation with the X-FEM method. In this presentation, application to transient machining simulations will be illustrated. [less ▲]

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See detailVorosweep: a fast generalized crystal growing Voronoi diagram generation algorithm
Mouton, Thibaud; Béchet, Eric ULg

E-print/Working paper (2014)

We propose a new algorithm for generating quickly approximate generalized Voronoi diagrams of point sites associated to arbitrary convex distance metric in the Euclidian plane. This algorithm produces ... [more ▼]

We propose a new algorithm for generating quickly approximate generalized Voronoi diagrams of point sites associated to arbitrary convex distance metric in the Euclidian plane. This algorithm produces connected cells by emulating the growth of crystals starting at the point sites, in order to reduce the complexity of the diagram. The main practical contribution is the Vorosweep package which is the reference implementation of the algorithm. Experimental results and benchmarks are given to demonstrate the versatility of this approach. [less ▲]

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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

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See detailIntégration de la méthode XFEM dans le processus de CAO
François, Vincent; Béchet, Eric ULg; Cuillière, Jean-Christophe

in actes du 11ème colloque national en calcul des structures (2013, May)

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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: 116 (40 ULg)