Hierarchical Stochastic Homogenization Analysis of a Short-Fiber Reinforced Composite Material Considering a Non-Uniform Microscopic Random Variation

Abstract

This paper discusses a stochastic homogenization analysis problem of a unidirectionally aligned short fiber reinforced composite material considering a uniform and/or non-uniform random variation of a microscopic quantity such as a material property or volume fraction of a microstructure. The homogenization analysis is performed with the homogenization theory and the equivalent inclusion method, and the stochastic analysis is performed with the perturbation-based method. In order to analyze the stochastic homogenization problem considering a periodic non-uniform microscopic random variation of the microscopic quantity, the hierarchical stochastic homogenization analysis procedure is proposed. As an example, the stochastic homogenization problems considering a non-uniform random variation of Young's modulus of resin and volume fraction of fiber are solved. From the numerical results, influence of the non-uniformity of the microscopic random variation is discussed. Also, from comparison between the results obtained with the proposed method and the Monte-Carlo simulation, accuracy of the proposed approach for the stochastic homogenization analysis of the short fiber reinforced composite material is discussed.