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Topological optimization of complex heterogeneous materials

Abstract : 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
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Daicong Da. Topological optimization of complex heterogeneous materials. Materials. Université Paris-Est; Hunan agricultural university, 2018. English. ⟨NNT : 2018PESC1102⟩. ⟨tel-02085825⟩

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