Hierarchical stochastic homogenization analysis of a particle reinforced composite material considering non-uniform distribution of microscopic random quantities

Abstract

This paper discusses a stochastic homogenization problem for evaluation of stochastic characteristics of a homogenized elastic property of a particle reinforced composite material especially in case of considering a nonuniform distribution of a material property or geometry of a component material and its random variation. In practice, some microscopic random variations in composites may not be uniform. In this case, a non-uniformly distributed random variation of a microscopic material or geometrical property should be taken into account. For this problem, this paper proposes a hierarchical stochastic homogenization method. This method assumes that a two-phase composite material can be separated into three-scales, and propagation of the randomness through the different scales can be evaluated with the perturbation-based technique. As an example, stochastic characteristics of homogenized elastic properties of a glassparticle reinforced plastic are estimated using the proposed approach. With the numerical results, importance of the problem and validity of the proposed method are discussed.

A successive perturbation-based multiscale stochastic analysis method for composite materials

“…There are many difficulties such as the number of random variables and their correlations, which should be overcome for employing an efficient method. Since a simplified analysis of this type problems with the hierarchical stochastic homogenization method [26] has been reported, which is based on the perturbation-based approach, the presented successive perturbation method will be extended to multiscale stochastic analysis for non-uniform randomness in a next step of this study.…”

Multiscale Stochastic Stress Analysis of a Porous Material with the Perturbation-Based Stochastic Homogenization Method for a Microscopic Geometrical Random Variation

“…In particular, the perturbation-based approach should be carefully used for the location variation of the holes, and it is considered that an effective method should be developed for improving the accuracy of the estimation. In addition, for a more practical problem, a non-uniform microscopic random variation (12) should be taken into account in a next step of this study.…”

A Multiscale Stochastic Stress Analysis of a Heterogeneous Material considering Nonuniform Microscopic Random Variation

“…Comparing the results to the case of stochastic homogenization considering a nonuniform microscopic random variation (12) , the influence of the CV nonuniformity is considerable, thus highlighting the importance of considering the nonuniform microscopic random variation in multiscale stochastic stress analysis for evaluating the reliability of a structure made from a heterogeneous material.…”

“…As described above, a randomly distributed quantity in one structure is not considered in this study. An example of a related study would be stochastic homogenization analysis considering a nonuniform random variation in a composite material (12) . However, influence of the nonuniformity of a microscopic random variation in a heterogeneous material on the probabilistic response of microscopic stresses has not been studied using multiscale stochastic stress analysis.…”