On Multi-scale Computational Design of Structural Materials Using the Topological Derivative

Abstract

This work deals on the optimization and computational material design using the topological derivative concept. The necessary details to obtain the anisotropic topological derivative are first presented. In the context of multi-scale topology optimization, it is crucial since the homogenization of the constitutive tensor of a micro-structure confers in general an anisotropic response. In addition, this work addresses the multi-scale material design problem in which the goal is then to minimize the structural (macro-scale) compliance by appropriately designing the material distribution (micro-structure) at a lower scale (micro-scale). To overcome the exorbitant computational cost, a consultation during the iterative process of a discrete material catalog (computed off-line) of micro-scale optimized topologies (Computational Vademecum) is proposed in this work. This results into a large diminution of the resulting computational costs, which make affordable the proposed methodology for multi-scale computational material design. Some representative examples assess the performance of the considered approach.