Hierarchical stochastic homogenization analysis of a particle reinforced composite material considering non-uniform distribution of microscopic random quantities

Abstract

This paper discusses a stochastic homogenization problem for evaluation of stochastic characteristics of a homogenized elastic property of a particle reinforced composite material especially in case of considering a non-uniform distribution of a material property or geometry of a component material and its random variation. In practice, some microscopic random variations in composites may not be uniform. In this case, a non-uniformly distributed random variation of a microscopic material or geometrical property should be taken into account. For this problem, this paper proposes a hierarchical stochastic homogenization method. This method assumes that a two-phase composite material can be separated into three-scales, and propagation of the randomness through the different scales can be evaluated with the perturbation-based technique. As an example, stochastic characteristics of homogenized elastic properties of a glass-particle reinforced plastic are estimated using the proposed approach. With the numerical results, importance of the problem and validity of the proposed method are discussed.