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The present article introduces an automated procedure to construct geometrical Representative Volume Elements (RVE) of open-foam cellular materials from computerized tomography (CT) images, with the final aim of generating meshable geometries usable in the Finite Element Method (FEM) used in order to analyse their mechanical behaviour. The methodology consists in growing and fitting a set of ellipsoids to each of the foam cells. These ellipsoids are seeded by local maxima of the distance to the struts obtained from computer tomography images. This methodology is thus fully voxel-based and does not depend on any assumption about statistical distributions of the foam cells. Therefore, it is able to reproduce an accurate geometrical model of the foam's microstructure and its possible irregularities. Moreover, this procedure allows the processing of large 3D data sets that do not fit the random access memory (RAM) by slicing it into smaller independent chunks. The effectiveness of the proposed approach is illustrated by comparing it to FEM simulations for which meshes are obtained from a feature reconstruction approach. Both FEM simulations are then compared with experimental results of uniaxial compressions of an open foam., info:eu-repo/semantics/published

The ductile fracture behavior of a high strength steel is investigated using a micromechanicsbased approach with the objective to build a predictive framework for the fracture strain and crack propagation under different loading conditions. Part I of this study describes the experimental results and the determination of the elastoplastic behavior and damage nucleation under different stress triaxiality and Lode parameter values. The damage mechanism starts early void nucleation from elongated inclusions, either by particle cracking under loading oriented along the major axis, or by matrix decohesion when the main loading is transverse. Void nucleation is followed by plastic growth and coalescence. The long inclusion axis is preferentially aligned in one direction leading to significant failure anisotropy with the fracture strain in the transverse direction being almost 50% lower compared to the longitudinal one, even though the plastic behavior is isotropic. The experimental data are first used to calibrate the elastoplastic model. An enhanced anisotropic nucleation model is then developed and integrated into the Gurson–Tvergaard–Needleman scheme. The parameters identification of the anisotropic nucleation model is finally performed and validated towards the experimental results. All these elements are subsequently used in Part II to simulate the full failure behavior of all testing specimens in the entire spectrum of stress states, from nucleation to final failure.

The ductile fracture behavior of a high strength steel is addressed in this two-part study using a micromechanics-based approach. The objective of Part II is to propose, identify, and validate a numerical model of ductile fracture based on the Gurson–Tvergaard–Needleman model. This model is enhanced by the Nahshon–Hutchinson shear modification in combination with a generalization of the Thomason coalescence criterion within a fully nonlocal form and relying on a damage-to-crack transition technique. The material model involves parameters of different natures either related to the micro-mechanics of porous materials or to semi-empirical formalisms. The void nucleation model and elastoplastic behavior have been developed and identified in Part I. The other parameters are identified in this part using inverse modeling based on both the numerical results of void cell simulations and the experimental measurements. The model is shown to adequately predict the effect of stress triaxiality and Lode parameter on the fracture strain as well as the fracture anisotropy. While the cup-cone and slant fracture paths in the round bars and in the plane strain specimens, respectively, cannot be captured using the pure continuum approach, the damage-to-crack transition framework reproduces these experimental observations.

In this work, a Representative Volume Element (RVE) generator based on the distance fields of arbitrary shaped inclusion packing is used to obtain morphologies of open-foam materials. When the inclusions are spherical, the tessellations of the resultant packing creates morphologies that are similar to physical foam samples in terms of their face-to-pore ratio, edge-to-face ratio and strut length distribution among others. Functions that combine the distance fields can be used to obtain the tessellations along with the necessary variations in the strut geometry and extract these open-foam morphologies. It is also possible to replace the inclusion packing with a predefined set of inclusions that are directly extracted from CT-scan based images.The use of discrete level-set functions results in steep discontinuities in the distance function derivatives. A multiple level-set based approach is presented that can appropriately capture the sharp edges of the open-foam struts from the resultant distance fields. Such an approach can circumvent the discontinuities presented by the distance fields which might lead to spurious stress concentrations in a material behavior analysis.The individual cells are then extracted as inclusion surfaces based on said combinations of the distance functions and their modifications. These surfaces can be joined together to obtain the final geometry of the open-foam morphologies. The physical attributes of the extracted geometries are compared to the experimental data. A statistical comparison is presented outlining the various features. The study is extended to morphologies that have been extracted using CT-scan images. With the help of mesh optimization tools, surface triangulations can be obtained, merged and developed as finite element (FE) models. The models are ready to use in a multi-scale study to obtain the homogenized material behavior. The upscaling can help assess the practical applications of these models by comparing with experime, Dans ce travail, un générateur de volumes élémentaires représentatifs (VER) basé sur les champs de distance d'un agrégat d'inclusions de forme arbitraire est développé dans le cadre de matériaux moussés à structure ouverte. Lorsque les inclusions sont sphériques, la tessellation de l'agrégat résulte en des morphologies similaires aux échantillons de mousse physique en termes de rapports des nombres de face par pores et de bords par faces, ainsi que de la distribution de la longueur des entretoises, entre autres. Les fonctions qui combinent les champs de distance peuvent être utilisées pour obtenir des tesselations avec les variations nécessaires aux géométries des entretoises et extraire ces morphologies de mousse ouverte. Il est également possible de remplacer l'agrégat d'inclusions par un ensemble prédéfini d'inclusions qui sont directement extraites d'images tomographiques.L'utilisation de fonctions de niveaux discrètes entraîne de fortes discontinuités dans les dérivées des champs de distance. Une approche basée sur des ensembles de niveaux multiples est présentée qui peut capturer de manière appropriée les arêtes vives des entretoises des mousses ouvertes à partir des champs de distance résultants. Une telle approche peut contourner les discontinuités présentées par les champs de distance qui pourraient conduire à des concentrations de contraintes parasites dans une analyse ducomportement des matériaux.Les pores individuels sont ensuite extraits en tant que surfaces d'inclusions sur la base desdites combinaisons des fonctions de distance et de leurs modifications. Ces surfaces peuvent être réunies pour obtenir la géométrie finale des morphologies de mousse ouverte. Les attributs physiques des géométries extraites sont comparés aux données expérimentales. Une comparaison statistique est présentée décrivant les différentes caractéristiques. L'étude est étendue aux morphologies qui ont été extraites à l'aide d'images tomographiques.À l'aide d'outils d'optimisation, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

The mechanical behavior of closed cell metallic foams strongly depends on their geometry at the scale of cells and cell walls. Two approaches are proposed in this work to address this computationally:(i) a controlled geometrical description of foam morphology features by exploiting an advanced tessellation-based procedure, allowing to generate realistic microstructural geometry,(ii) a procedure allowing to extract geometrical features of a foam morphology based on image-based modelling using CT scans. The first approach proposes a methodology that allows the automated generation of RVEs with a detailed control of the microstructure, including of cell geometries. It is primarily based on an inclusions packing algorithm assisted by distance fields control. Such distance fields can subsequently be used to morph inclusions, producing generalized tessellations with the possibility of incorporating curved and irregular boundaries. 3D morphologies of closed cell foams are produced by extracting the geometry from a proper combination of distance field functions. The procedure allows controlling the cell size distribution, spatial cell wall thickness distribution (correlated or not with the cell size distribution), wall curvatures and/or defects. An automated 3D meshing tool for implicit geometries was exploited to produce high quality tetrahedral meshes from the generated implicit foam geometries. Representative volume element based simulations were performed using this approach to assess the different morphological features relative importance on the mechanical behaviour of ALPORAS. An original extension of this tool was incorporating the transformation of 3D geometry into a shell-based finite element model. This resulted in a significant gain in computation time and allowed for simulating compression test up to densification (being out of reach with 3D solid finite element models) showing a good qualitative match with experimental results from the literature.The second ap, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

Numerical prediction of woven composites mechanical properties has been a challenge since decades. Accurate prediction of these mechanical properties lies in the fidelity of the numerical geometries with respect to the real composite microstructure. There are many methods for woven composite geometry generation but they are mostly limited by the residual interpenetrations between yarns which prevent from a discretization conform to the yarns geometries. In a first step of the present research, an automated method for 3D complex woven composites generator is developed. The generation procedure consists of defining an initial situation of yarns made by discretized straight lines with a polygonal cross section attached to each node. A straightening operation consisting of progressive nodal displacement iteratively with a contact management operation is used until the yarns reach their equilibrium position in the RVE. There could remain some minor residual interpenetrations in the obtained RVEs, so a level set based post-processing tool is used systematically after the generation process to suppress the residual interpenetrations, control the yarns volume fractions and insert a thin gap between the yarns for a further discretization conform to the yarns geometry. The discretization tool used subsequently to the geometry generation process uses the analogy to truss structures to generate a high quality tetrahedral mesh for finite elements simulations. Woven composites geometries can also be obtained by exploiting the 3D images of μCT scans. Voxel-based discretizations obtained from image segmentation are nowadays more and more used straightforwardly for mechanical simulations of the behavior of woven composites. The main advantage of this discretization technique is to generate fast regular hexahedral meshes without interpenetrations, that allows producing accurate homogenized elastic properties with acceptable voxel sizes. However, the use of voxel geometries may be que, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

We present a stochastic approach combining Bayesian Inference (BI) with homogenization theories in order to identify, on the one hand, the parameters inherent to the model assumptions and, on the other hand, the composite material constituents behaviors, including their variability. In particular, we characterize the model parameters of a Mean-Field Homogenization (MFH) model and the elastic matrix behavior, including the inherent dispersion in its Young's modulus, of non-aligned Short Fibers Reinforced Polymer (SFRP) composites. The inference is achieved by considering as observations experimental tests conducted at the SFRP composite coupons level. The inferred model and material law parameters can in turn be used in Mean-Field Homogenization (MFH)-based multi-scale simulations and can predict the confidence range of the composite material responses.

The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress–strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress–strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions.

We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in the strain measurements. Since a difference between the model and the experimental data may still be present if the data is not contaminated by noise, we also incorporate the possible error of the model itself. The three formulations to describe model uncertainty in this contribution are: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. Our results show that incorporating model uncertainty often, but not always, improves the results. If the error in the strain is considered as well, the results improve even more.

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This paper presents an automated approach to build computationally Representative Volume Elements (RVE) of open-foam cellular materials, enabling the study of the effects of the microstructural features on their macroscopic behavior. The approach strongly relies on the use of distance and level set functions. The methodology is based on the extraction of random tessellations from inclusion packings following predetermined statistical packing distribution criteria. With the help of simple recombination operations on the distance fields, the tessellations are made to degenerate in Laguerre tessellations. Predetermined morphological characteristics like strut cross-section variation based on commercially available materials are applied on the RVE to ensure the extraction of closely matching models using simple surface extraction tools, and a detailed morphology quantification of the resulting RVEs is provided by comparing them with experimental observations. The extracted RVE surface is then treated with smoothening criteria before obtaining a 3D tetrahedralized model. This model can then be exported for multi-scale simulations to assess the effects of microstructural features by an upscaling methodology. The approach is illustrated by the simulation of a compression test on an RVE incorporating plasticity with geometrically non-linear behavior., SCOPUS: ar.j, info:eu-repo/semantics/published

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3D reinforced composites are favored for aerospace, automotive and wind turbine applicationbecause of their high specific stiffness and strength in the in-plane and out-ofplanedirections. In these composites, pins, stitching yarns and binder yarns are insertedthrough-the-thickness of the in-plane fiber-reinforced regions. Binder parameters as diameter,content, pattern and tensioning can further be varied to regulate the out-of-planeproperties. However, the insertion of these binders distorts the reinforcement which furthercan affect the global and local mechanical behaviour. Unit-cell models offered avaluable approach to assess the effect of the distortions on these mechanical features.An approach is presented to include the main geometrical features of pinned, stitchedand 3D woven composites into mesoscopic unit-cell models. Discretised lines, whichrepresent the main geometrical features, are hereby gradually shaped by geometrical operationswhile a geometrical contact treatment account for line interactions. The localfiber volume fraction and fiber direction distributions are afterwards modelled on crosssectionsin a post-processing step. Tools are further proposed to automatically transformthe geometrical models into finite element models. The effect of distortions, local fibervolume fraction and fiber direction, and typical geometrical features for each 3D reinforcedcomposite, on the stiffness and damage initiation stress levels is investigated bymeans of elastic finite element (FE)-computations.The shape of geometrical features corresponding to the different binder parameters couldautomatically be generated and the dimensions of features could be controlled by the parametersof the geometrical operations. The stiffness of a 3D reinforced composite havebeen observed to be either decreased or increased (dependent on the stacking sequence,the binder type and the loading direction). Early damage initiation in the FE-modelswas observed to take place near the binder loc, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

info:eu-repo/semantics/nonPublished

The principal objective of this thesis is to predict the response of inelastic materials under a large number of cycles, while simulating a much smaller number. For coupled viscoelastic-viscoplastic (VE-VP) homogeneous solids subjected to large numbers of cycles, a two-scale time homogenization formulation and the corresponding algorithms are proposed. The main aim is to predict the long time response while reducing the computational cost considerably. The method is based on the definition of macro and micro-chronological time scales, and on asymptotic expansions of the unknown variables. First, the VE-VP constitutive model is formulated based on a thermodynamical framework. Next, the original VE-VP initial-boundary value problem is decomposed into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The former is purely VE, and solved once for each macro time step, whereas the latter problem is nonlinear and solved iteratively using fully implicit time integration. For micro-scale time averaging, one-point and multi-point integration algorithms are developed. Several numerical simulations on uniaxial and multiaxial cyclic loadings illustrate the computational efficiency and the accuracy of the proposed methods. For composite materials, a multiscale computational strategy is proposed for the analysis of structures, which are described at a refined level both in space and in time. The proposal is applied to two-phase VE-VP composite materials subjected to large numbers of cycles. The main aim is to predict the effective long time response while reducing the computational cost considerably. The proposed computational framework is a combination of the mean-field space homogenization based on the generalized incrementally affine formulation for VE-VP composites, and the asymptotic time homogenization approach for coupled VE-VP homogeneous solids under large numbers of cycles. The time homogenization method is based on the def, (FSA - Sciences de l'ingénieur) -- UCL, 2016

Micro-electro-mechanical systems (MEMS) made of polycrystalline silicon are widely used in several engineering fields. The fracture properties of polycrystalline silicon directly affect their reliability. The effect of the orientation of grains on the fracture behaviour of polycrystalline silicon is investigated out of the several factors. This is achieved, firstly, by identifying the statistical variation of the fracture strength and critical strain energy release rate, at the nanoscopic scale, over a thin freestanding polycrystalline silicon film having mesoscopic scale dimensions. The fracture stress and strain at the mesoscopic level are found to be closely matching with uniaxial tension experimental results. Secondly, the polycrystalline silicon film is considered at the continuum MEMS scale, and its fracture behaviour is studied by incorporating the nanoscopic scale effect of grain orientation. The entire modelling and simulation of the thin film is achieved by combining the discontinuous Galerkin method and extrinsic cohesive law describing the fracture process., Belgian National Foundation for Scientific Research (FRFC 2.4508.11), Belgian National Foundation for Scientific Research (PDR T.0122.13 “MECANO”)

Micro-electro-mechanical systems (MEMS) made of polycrystalline silicon are widely used in several engineering fields. The fracture properties of polycrystalline silicon directly affect their reliability. The effect of the orientation of grains on the fracture behaviour of polycrystalline silicon is investigated out of the several factors. This is achieved, firstly, by identifying the statistical variation of the fracture strength and critical strain energy release rate, at the nanoscopic scale, over a thin freestanding polycrystalline silicon film having mesoscopic scale dimensions. The fracture stress and strain at the mesoscopic level are found to be closely matching with uniaxial tension experimental results. Secondly, the polycrystalline silicon film is considered at the continuumMEMSscale, and its fracture behaviour is studied by incorporating the nanoscopic scale effect of grain orientation. The entire modelling and simulation of the thin film is achieved by combining the discontinuous Galerkin method and extrinsic cohesive law describing the fracture process.

The aim of this work is to develop an efficient large-strain hyperelastic constitutive model for amorphous polymers in the glassy state. These materials exhibit a complex rate-and pressure-sensible behavior in both elastic and plastic regimes. After an initial linear elastic region, a nonlinear stage continues until reaching a peak stress, which is followed by a softening stage. At large strains, when the softening is saturated, a re-hardening stage is reached. The viscoelastic effect is captured using the generalized Maxwell model. The viscoplastic effect is considered using a Perzyna-type flow rule incorporating a pressure sensitive yield surface and a non-associated flow potential. This yield surface is extended from the Drucker-Prager one. The saturated softening phenomenon is modeled using an isotropic numerical damage variable progressed by a saturated softening law. With the introduction of the damage parameter, a non-local implicit gradient damage model is used to avoid the loss of the solution uniqueness. Through experimental comparisons, it is shown that the proposed model has the ability to model the complex mechanical responses of amorphous glassy polymers

Because of their widely generalized use in many industries, composites are the subject of many research campaigns. More particularly, the development of both accurate and flexible numerical models able to capture their intrinsically multiscale modes of failure is still a challenge. The standard finite element method typically requires intensive remeshing to adequately capture the geometry of the cracks and high accuracy is thus often sacrificed in favor of scalability, and vice versa. In an effort to preserve both properties, we present here an extended finite element method (XFEM) for large scale composite fracture simulations. In this formulation, the standard FEM formulation is partially enriched by use of shifted Heaviside functions with special attention paid to the scalability of the scheme. This enrichment technique offers several benefits since the interpolation property of the standard shape function still holds at the nodes. Those benefits include (i) no extra boundary condition for the enrichment degree of freedom, and (ii) no need for transition/blending regions; both of which contribute to maintaining the scalability of the code. Two different cohesive zone models (CZM) are then adopted to capture the physics of the crack propagation mechanisms. At the intralaminar level, an extrinsic CZM embedded in the XFEM formulation is used. At the interlaminar level, an intrinsic CZM is adopted for predicting the failure. The overall framework is implemented in ALYA, a mechanics code specifically developed for large scale, massively parallel simulations of coupled multi-physics problems. The implementation of both intrinsic and extrinsic CZM models within the code is such that it conserves the extremely efficient scalability of ALYA while providing accurate physical simulations of computationally expensive phenomena. The strong scalability provided by the proposed implementation is demonstrated. The model is ultimately validated against a full experimental campaig, A.J., A.M., D.T., L.N. and L.W. acknowledge funding through the SIMUCOMP ERA-NET MATERA + project financed by the Fonds National de la Recherche (FNR) of Luxembourg, the Consejería de Educación y Empleo of the Comunidad de Madrid, the Walloon region (agreement no 1017232, CT-EUC 2010–10-12), and by the European Unions Seventh Framework Programme (FP7/2007–2013)., Peer Reviewed, Postprint (author's final draft)

© 2015 Elsevier Ltd. Because of their widely generalized use in many industries, composites are the subject of many research campaigns. More particularly, the development of both accurate and flexible numerical models able to capture their intrinsically multiscale modes of failure is still a challenge. The standard finite element method typically requires intensive remeshing to adequately capture the geometry of the cracks and high accuracy is thus often sacrificed in favor of scalability, and vice versa. In an effort to preserve both properties, we present here an extended finite element method (XFEM) for large scale composite fracture simulations. In this formulation, the standard FEM formulation is partially enriched by use of shifted Heaviside functions with special attention paid to the scalability of the scheme. This enrichment technique offers several benefits since the interpolation property of the standard shape function still holds at the nodes. Those benefits include (i) no extra boundary condition for the enrichment degree of freedom, and (ii) no need for transition/blending regions; both of which contribute to maintaining the scalability of the code.Two different cohesive zone models (CZM) are then adopted to capture the physics of the crack propagation mechanisms. At the intralaminar level, an extrinsic CZM embedded in the XFEM formulation is used. At the interlaminar level, an intrinsic CZM is adopted for predicting the failure. The overall framework is implemented in ALYA, a mechanics code specifically developed for large scale, massively parallel simulations of coupled multi-physics problems. The implementation of both intrinsic and extrinsic CZM models within the code is such that it conserves the extremely efficient scalability of ALYA while providing accurate physical simulations of computationally expensive phenomena. The strong scalability provided by the proposed implementation is demonstrated. The model is ultimately validated against a full

Micro-electro-mechanical systems (MEMS) made of polycrystalline silicon are widely used in several engineering fields. The fracture properties of polycrystalline silicon directly affect their reliability. The effect of the orientation of grains on the fracture behaviour of polycrystalline silicon is investigated out of the several factors. This is achieved, firstly, by identifying the statistical variation of the fracture strength and critical strain energy release rate, at the nanoscopic scale, over a thin freestanding polycrystalline silicon film having mesoscopic scale dimensions. The fracture stress and strain at the mesoscopic level are found to be closely matching with uniaxial tension experimental results. Secondly, the polycrystalline silicon film is considered at the continuum MEMSscale, and its fracture behaviour is studied by incorporating the nanoscopic scale effect of grain orientation. The entire modelling and simulation of the thin film is achieved by combining the discontinuous Galerkin method and extrinsic cohesive law describing the fracture process., SCOPUS: ar.j, info:eu-repo/semantics/published