Topology optimization of particle-matrix composites for optimal fracture resistance taking into account interfacial damage

AcceptedInternational audienceThis 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

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry-property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from geometry to properties. We further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (relative error <5%) and 2) improve the optimized structural performance over the conventional topology-optimized variable-density structure. Specifically, in the minimum compliance example, our IH-GAN generated structure achieves an 84.4% reduction in concentrated stress and an extra 7% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 24.2% and 44.4% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending

Topology optimization of periodic lattice structures taking into account strain gradient

International audienceWe present a topology optimization for lattice structures in the case of non-separated scales, i.e. when the characteristic dimensions of the periodic unit cells in the lattice are not much smaller than the dimensions of the whole structure. The present method uses a coarse mesh corresponding to a homogenized medium taking into strain gradient through a non-local numerical homogenization method. Then, the topological optimization procedure only uses the values at the nodes of the coarse mesh, reducing drastically the computational times. We show that taking into account the strain gradient within the topological optimization procedure brings significant increase in the resulting stiffness of the optimized lattice structure when scales are not separated, as compared to using a homogenized model based on the scale separation assumption

Optimisation topologique de matériaux complexes hétérogènes

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 resistanceLes 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 structur

Topology Optimization for Maximizing the Fracture Resistance of Periodic Quasi-Brittle Composites Structures

International audienceTopology 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

Topology optimization of composite structures for fracture resistance with phase field modeling of crack propagation

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Topology optimization for maximizing the fracture resistance of quasi-brittle composites

International audienceIn this paper, we propose a numerical framework for optimizing the fracture resistance of quasi-brittle composites through a modification of the topology of the inclusion phase. The phase field method to fracturing is adopted within a regularized description of discontinuities, allowing to take into account cracking in regular meshes, which is highly advantageous for topology optimization purpose. Extended bi-directional evolutionary structural optimization (BESO) method is employed and formulated to find the optimal distribution of inclusion phase, given a target volume fraction of inclusion and seeking a maximal fracture resistance. A computationally efficient adjoint sensitivity formulation is derived to account for the whole fracturing process, involving crack initiation, propagation and complete failure of the specimen. The effectiveness of developed framework is illustrated through a series of 2D and 3D benchmark tests