非一様な微視的ばらつきを有する短繊維強化複合材料の階層型確率均質化解析

概要

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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 Youngs 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.