A framework for optimal microstructural design of random heterogeneous materials

Abstract

An efficient micromechanical methodology is developed for tailoring elastic and thermal properties of random heterogeneous materials. The methodology involves three steps: (i) statistical reconstruction based on the two-point correlation function (TPCF), (ii) thermomechanical homogenization, and (iii) optimization. The method relies on the tailoring the state of anisotropy of the microstructure to achieve desired directional effective properties. This capability is demonstrated by designing heterogeneous microstructures with optimal elastic modulus and thermal conductivity in perpendicular directions. The study aims at presenting optimal computational algorithms for the reconstruction, homogenization and optimization steps. Several studies study are presented to demonstrate the feasibility of obtaining desired thermomechanical properties with a minimal set of design variables. These case studies highlight the advantages and limitations of the method, along with its computational cost.