摂動法に基づくマルチスケール確率応力解析法を用いた粒子強化複合材料の微視的材料定数変動に対する破壊確率解析

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This paper describes a stochastic multiscale stress analysis and failure probability analysis of a particle reinforced composite material via the stochastic homogenization analysis. In order to validate a numerical result based on the computational methodology, the importance of the probabilistic analysis in computational mechanics has been noticed in recent. In particular, we focus on the computational procedure for estimation of uncertainty propagation through the different scales in a heterogeneous material, and the influences of a microscopic random variation of elastic properties of component materials on the microscopic stress field and microscopic failure probability are investigated. The Monte-Carlo simulation and the perturbation-based approach are employed for the stochastic analysis, and the homogenization-theory based finite element analysis is employed for the multiscale stress analysis. With the numerical results, the influences of the microscopic random variation of the elastic properties are investigated, and applicability of the perturbation-based approach is discussed. From the results, the importance of the presented multiscale stochastic stress analysis and the failure probability analysis considering the microscopic random variation for a heterogeneous material will be illustrated.