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Experimental and computational micro–mechanical investigations of compressive properties of polypropylene/multi–walled carbon nanotubes nanocomposite foams ; ; Leblanc, Christophe 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 ▲] Detailed reference viewed: 182 (61 ULg)Numerical simulations on embedded solids : integration of CAD and eXtended Finite Element Analysis Duboeuf, Frédéric ; Béchet, Eric 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 ▲] Detailed reference viewed: 43 (11 ULg)Simulations numériques sur des solides plongés, dans un contexte X-FEM Duboeuf, Frédéric ; Béchet, Eric Conference (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 ▲] Detailed reference viewed: 53 (19 ULg)Streamable Laguerre-Voronoi Tessellation Model for Tomographic Images Leblanc, Christophe ; Nguyen, Van Dung ; 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: 55 (27 ULg)Embedded solids of any dimensions in the extended finite element method Duboeuf, Frédéric ; Béchet, Eric 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 ▲] Detailed reference viewed: 38 (8 ULg)Vorosweep: a fast generalized crystal growing Voronoi diagram generation algorithm ; Béchet, Eric 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 ▲] Detailed reference viewed: 99 (39 ULg)Fifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) Béchet, Eric ; ; Geuzaine, Christophe et al in International Journal of Computational & Applied Mathematics (2013), 246 Detailed reference viewed: 167 (37 ULg)A Frontal Delaunay Quad Mesh Generator Using the L ∞ Norm ; ; et al in International Journal for Numerical Methods in Engineering (2013), 94(5), 494-512 Detailed reference viewed: 108 (38 ULg)Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation Nguyen, Van Dung ; Béchet, Eric ; Geuzaine, Christophe 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: 658 (315 ULg)Lloyd relaxation using analytical Voronoi diagram in the L_infinite norm and its application to quad optimization Mouton, Thibaud ; Béchet, Eric 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: 27 (12 ULg)The extended finite element method for three-dimensional reinforced composites. Duboeuf, Frédéric ; Béchet, Eric 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: 79 (29 ULg)Conversion of a B-Rep CAD model to an implicit representation in the context of the X-FEM Mouton, Thibaud ; Béchet, Eric 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: 20 (4 ULg)Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) Hogge, Michel ; ; et al Book published by Université de Liège - Dépôt légal: D/2011/0480/31 (2011) Detailed reference viewed: 46 (7 ULg)Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation Nguyen, Van Dung ; Béchet, Eric ; Geuzaine, Christophe 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: 129 (62 ULg)A Frontal Delaunay Quad Mesh Generator Using the L ∞ Norm ; ; et al in Proceedings of the 20th International Meshing Roundtable (2011, October) Detailed reference viewed: 54 (11 ULg)Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces ; ; Béchet, Eric 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: 47 (5 ULg)Calculs de structures basés sur la technique des level sets et la méthode de partition de l'unité ; Béchet, Eric ; et al in Actes du 9ème Colloque National en Calcul des Structures (2009, May) Detailed reference viewed: 17 (1 ULg)Some numerical experiments about cracked piezoelectric media Béchet, Eric ; (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: 35 (5 ULg)Application of the X-FEM to the fracture of piezoelectric materials Béchet, Eric ; ; 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: 46 (10 ULg)Simulations in ambient space : freeing mesh generation techniques from the respect of boundaries in the context of the FEM Béchet, Eric ; ; 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: 95 (13 ULg) |
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