Novel material anisotropy optimization based upon granular micromechanics

We propose an evolutionary algorithm that seeks to determine the optimal anisotropy of a deforming body in response to a given applied mechanical load, under the constraint of assigned mass. The algorithm is based for the first time upon a granular micromechanics approach to determine the effective material behavior, making use of an orientation-dependent distribution of normal and tangential elastic grain-grain interactions, whose associated stiffnesses are assumed to depend on an orientation-dependent angular mass density. This novel idea is intrinsically simple and takes advantage of both those penalization techniques, that are generally used in topological optimization, and on those basic concepts of continuum granular micromechanics that are particularly prone to be used in this field. The algorithm is initialized with an isotropic distribution of mass such that the total mass exceeds the desired one. Grain-grain interaction stiffnesses along orientations that are only lightly stressed by the applied load are penalized and the angular mass density is accordingly reduced along these orientations. This yields a non-uniform orientation-dependent mass density and, in turn, an anisotropic constitutive law. The proposed algorithm is numerically evaluated for two load cases implying homogeneous deformations and the response to loading produced by the optimal effective fourth-rank elasticity tensor is compared with that obtained by isotropic angular mass density reduction. The proposed algorithm can be employed for engineering microstructures and as a building block for topology optimization algorithms.