等価介在物法を用いた一次摂動解析による球形粒子強化複合材料の確率均質化解析

概要

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This paper describes a method for stochastic homogenization analysis of a particle reinforced composite material. Since it is difficult to apply the homogenization-based perturbation method using the finite element method to a stochastic homogenization problem with considering a microscopic geometrical random variation in a microstructure, the equivalent inclusion method is used for the perturbation-based stochastic homogenization analysis. In using the equivalent inclusion method, each perturbation term for a random variation in a material property, size of inclusions or their volume fraction can be computed analytically. This fact shows applicability to apply the proposed method to a stochastic homogenization problem considering the microscopic geometrical random variation. At first, formulations for the proposed method are introduced. Next, the proposed method is applied to several kinds of numerical examples. From the numerical results, validity and accuracy of the proposed method are confirmed.
2009-08-25