Hierarchical multiscale optimization of the microstructure arrangement and macroscopic topology in computational material design

A E. HUESPE; J. OLIVER,; A. FERRER; J. HERNANDEZ; J.C. CANTE

Barcelona

Congreso; COMPLAS XII, Int. Conf. on Comp. Plasticity, Fundamentals and Applic.,; 2013

Computational design of engineering materials accounting for their microstructure has gained considerable interest in the computational mechanics community. Whereas some single-scale optimization techniques (i.e. macroscopic topology of structures or the microscopic material arrangement) are nowadays relatively well established, simultaneous, hierarchically coupled, optimization of both scales is a promising research subject deserving further exploration. This work is an attempt to evaluate the performance of a numerical tool based on:a) A description of the material behaviour using a two-scale homogenization procedure [1].b) A continuum, gradient-based, optimization scheme based on the interior point method [2].In this scenario, a preliminary exploration of a numerical scheme for optimization of the arrangement of the material components in the microstructure is done. In a first step, the microstructure topology is considered fixed, and the material properties of the components (e.g. the Young modulus) are continuously described by means of a ?density-like? parameter, similarly to what is done in well established single-scale topological optimization procedures [3]. Then, values of that parameter, for all components in the RVE and, in turn, for all RVE?s are considered as the design variables (lying in the micro-scale). In addition, the objective function is defined at the macro-scale (e.g. minimum weight, maximum stiffness etc.), which, together with some restrictions, defines the optimization problem.Solution of this problem provides: a) a description of the optimal microstructure arrangement in every RVE, in terms of the distribution of the density-like parameter, b) the macroscopic, RVE-averaged, values of that parameter, supplying an indicator of the optimal topological description of the macrostructure. Therefore, this results into a combined two-scale optimization procedure, simultaneously providing the optimal microstructure arrangement at every point of the macrostructure and the optimal structure topology.A number of representative numerical simulations show the performance and possibilities of the proposed method.