Stochastic multiscale stress analysis via identification of microscopic randomness

This paper proposes a concept of a stochastic stress analysis procedure via identification of a microscopic random variation. Some results on a stochastic homogenization problem of composites have been reported, and those illustrate that a microscopic random variation in material property or geometry will have an influence on a homogenized property of composites. Similarly, the microscopic randomness causes a random variation of macroscopic and microscopic stress field. If the microscopic random variation is unknown, a method for estimating the microscopic random variation from a characteristic of a macroscopic random variation will be also needed. In this paper, a stochastic multiscale stress analysis with both approaches is introduced, and necessity of an inverse stochastic homogenization analysis and validity of the proposed approach are discussed.