Non-local modeling with asymptotic expansion homogenization of random materials

TL;DR

This paper develops a non-local homogenized model for 3D composite materials with randomly distributed inclusions, using asymptotic expansion homogenization that accounts for stochastic parameters, enhancing understanding of their macroscopic behavior.

Contribution

It introduces a stochastic parameter into AEH for modeling random composites, combining variational methods with mean-ergodicity to improve homogenization accuracy.

Findings

Successful modeling of random composite behavior

Enhanced homogenization method incorporating stochasticity

Insights into macroscopic properties of random materials

Abstract

The aim of this study is to build a non-local homogenized model for three-dimensional composites with inclusions randomly embedded within a matrix according to a stochastic point process w in a bounded open set associated with a suitable probability space). Both phases were linear elastic. Asymptotic expansion homogenization (AEH) was revisited by taking into account the stochastic parameter representing the inclusion centers distribution. The macroscopic behavior was then studied by combining the variational approach with the mean-ergodicity.