Numerical design of random micro-heterogeneous materials with functionally-graded effective thermal conductivities using genetic algorithms and the fast boundary Element Method

Abstract

This paper introduces a numerical methodology for the design of ran- dom micro-heterogeneous materials with functionally graded effective thermal con- ductivities (ETC). The optimization is carried out using representative volume el- ements (RVEs), a parallel Genetic Algorithm (GA) as optimization method, and a Fast Multipole Boundary Element Method (FMBEM) for the evaluation of the cost function. The methodology is applied for the design of foam-like microstructures consisting of random distributions of circular insulated holes. The temperature field along a material sample is used as objective function, while the spatial distribution of the holes is the design variable. There are presented details of the FMBEM and the GA implementations, their customizations and tune up, and the analysis for the sizing of the RVE. The effectiveness of the proposed methodology is demonstrated for two examples. Computed results are experimentally validated using ad-hoc devised experiments.