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International audience; Topology optimization for maximizing the fracture resistance of particle-matrix composites is investigated. The methodology developed in our previous works, combining evolutionary topology optimization and phase field method to fracture embedding interfacial damage, is applied and extended to periodic composites and multiple objectives. On one hand, we constrain the periodicity of unit cells geometry and conduct their topology optimization for one given load prescribed over the whole structure. On the other hand, we consider a single unit cell whose topology is optimized with respect to the fracture energy criterion when subjected to multiple loads. Size effects are investigated. We show that significant enhancement of the fracture resistance can be achieved for the studied composite structures by the present method. In addition, a first attempt to fracture resistance enhancement of a unit cell associated with a material is investigated for multiple loads, exhibiting a complex optimized microstructure.

Nous proposons dans ce travail une méthodologie pour maximiser la résistance de composites de type matrice/inclusions pour lesquelles l'endommagement prend la forme de microfissuration dans la matrice et les interfaces. Pour cela, une approche par optimisation topologique est adoptée, dans laquelle la fonction objectif est directement définie comme l'énergie de fracturation de la structure composite, et obtenue par un calcul complet de fissuration par champ de phase, depuis l'initiation des fissures jusqu'à la rupture de la structure. La méthode BESO est adoptée pour l'optimisation topologique des inclusions.

Mechanical and physical properties of complex heterogeneous materials are determined on one hand by the composition of their constituents, but can on the other hand be drastically modified by their microstructural geometrical shape. Topology optimization aims at defining the optimal structural or material geometry with regards to specific objectives under mechanical constraints like equilibrium and boundary conditions. Recently, the development of 3D printing techniques and other additive manufacturing processes have made possible to manufacture directly the designed materials from a numerical file, opening routes for totally new designs. The main objectives of this thesis are to develop modeling and numerical tools to design new materials using topology optimization. More specifically, the following aspects are investigated. First, topology optimization in mono-scale structures is developed. We primarily present a new evolutionary topology optimization method for design of continuum structures with smoothed boundary representation and high robustness. In addition, we propose two topology optimization frameworks in design of material microstructures for extreme effective elastic modulus or negative Poisson's ratio. Next, multiscale topology optimization of heterogeneous materials is investigated. We firstly present a concurrent topological design framework of 2D and 3D macroscopic structures and the underlying three or more phases material microstructures. Then, multiscale topology optimization procedures are conducted not only for heterogeneous materials but also for mesoscopic structures in the context of non-separated scales. A filter-based nonlocal homogenization framework is adopted to take into account strain gradient. Finally, we investigate the use of topology optimization in the context of fracture resistance of heterogeneous structures and materials. We propose a first attempt for the extension of the phase field method to viscoelastic materials. In addition, Phase field methods for fracture able to take into account initiation, propagation and interactions of complex both matrix and interfacial micro cracks networks are adopted to optimally design the microstructures to improve the fracture resistance, Les propriétés effectives mécaniques et physiques des matériaux hétérogènes dépendent d'une part de leurs constituants, mais peuvent également être fortement modifiées par leur répartition géométrique à l'échelle de la microstructure. L'optimisation topologique a pour but de définir la répartition optimale de matière dans une structure en vue de maximiser un ou plusieurs objectifs tels que les propriétés mécaniques sous des contraintes telles que la masse de matière. Récemment, les développements rapides de l'impression 3D ou d'autres techniques de fabrication additive ont rendu possible la fabrication de matériaux avec des microstructures "à la demande", ouvrant de nouvelles perspectives inédites pour la conception de matériaux. Dans ce contexte, les objectifs de cette thèse sont de développer des outils de modélisation et de simulation numériques pour concevoir des matériaux et des structures hétérogènes ayant des propriétés optimisées basés sur l'optimisation topologique. Plus précisément, nous nous intéressons aux points suivants. Premièrement, nous proposons des contributions à l'optimisation topologique à une seule échelle. Nous présentons tout d'abord une nouvelle méthode d'optimisation topologique avec évolution pour la conception de structures continues par description lisse de bords. Nous introduisons également deux techniques d'homogénéisation topologique pour la conception de microstructures possédant des propriétés effectives extrêmes et des « méta propriétés » (coefficient de Poisson négatif).Dans une seconde partie, des techniques multi échelle basées sur l'optimisation topologique sont développées. Nous proposons d'une part une approche concourante de structures hétérogènes dont les microstructures peuvent posséder plus de deux matériaux. Nous développons ensuite une approche d'optimisation topologique dans un cadre d'homogénéisation pour des échelles faiblement séparées, induisant des effets de gradient. Enfin dans une troisième partie, nous développons l'optimisation topologique pour maximiser la résistance à la fracture de structures ou de matériaux hétérogènes. La méthode de champs de phase pour la fracture est combinée à la méthode BESO pour concevoir des microstructures permettant d'augmenter fortement la résistance à la rupture. La technique prend en compte l'initiation, la propagation et la rupture complète de la structure

(Keynote lecture); International audience

Accepted; International audience; This paper presents a topology optimization framework for optimizing the fracture resistance of two-phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bi-directional evolutionary structural optimization (BESO) method. The sensitivity formulation accounts for the whole fracturing process involving cracks nucleation, propagation and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended BESO method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.

International audience; Concrete is an important constitutive material of nuclear power plants and waste storage structures whose mainrole is to ensure high level of performance regarding the required middle to long-term containment function. Assuch, creep and microcracking are known significant factors affecting the mechanical properties and the long termbehavior of concrete, and may call into question the safety of nuclear facilities. The accurate modelling of thesephenomena including their coupled effects have then to receive a special attention. We propose in this study toapply the relatively recent method making use of a phase field approach to reproduce the initiation and propagationof microcracking in concrete. This method rests on a diffuse description of the microcrack surfaces by one scalarvariable whose values result from a specific balance equation. As a main contribution, it is extended here andcoupled to a linear viscoelastic behavior to mimic the creep (and possibly shrinkage) of the material. A classicalgeneralized Maxwell model is retained for modelling this viscoelastic behavior. At first, an energy-based formulationis developed to express the equations governing both viscoelastic mechanical and phase field problems. In this firstattempt, only cracking due to extensions is considered. Different simple fracture criteria based on positive stressesor strains with and without threshold are applied and tested. The resulting approach is next implemented in the FEcode Cast3M so as to solve both systems of equations. Applications to a homogeneous material subject to loadingwith various durations and intensity are then analyzed and discussed with regard to the different crack driving statefunctions. In a second stage, 3D simulations of heterogeneous concrete samples made up of elastic aggregatesdispersed in a mortar matrix concentrating the viscoelastic behavior are performed. These numerical specimensare generated with polyhedral aggregates having various size and shapes, and which are randomly distributed in abox. The effects of the aggregate shape on the microcracking development and the macroscopic behavior ofsamples subject to creep loading are investigated. To this aim, different specimens are created with elongated andflattened polyhedral aggregates with given aspect ratio, and the obtained results are analyzed and confronted inparticular in terms of microcrack patterns.

International audience