Stochastic Homogenization Method for Composite Materials with Uncertain Microstructures.

Abstract

Composite materials are widely used because of their excellent functional properties. However, in practice, they have the disadvantage that their microstructural parameters vary uncertainly. In this paper, the authors will propose a new stochastic finite element procedure combined with the homogenization method for the efficient analysis of the stochastic nature of composite materials with uncertain microstructures. In the proposed procedure, the stochastic homogenization method (SHM), the first order perturbation technique and the first order second moment method are applied to the homogenization method. The SHM, which can be used to compute the expectation and variance of microscopic stresses as well as those of macroscopic stresses, is implemented in a deterministic homogenization analysis code based on the finite element method. The results of numerical analysis indicate that the proposed method is usefull from the points of view of both efficiency and accuracy.