Local probabilistic homogenization of two-dimensional model foams accounting for micro structural disorder

The objective of the present study is a numerical analysis of disorder effects in solid structural foams caused by their random irregular micro structure. Using a strain energy based concept, the effective material response is computed in a geometrically non-linear homogenization analysis. The probabilistic homogenization is based on the analysis of a large scale statistically representative volume element. The stochastic information about the scatter in the material response on the lowest possible level is generated by a subsequent division of the representative volume element in substructures consisting of a single cell wall intersection and parts of the adjacent cell walls. For each of the substructures, a homogenization analysis is performed. The results for the local effective stress and strain components are evaluated by means of stochastic methods. The approach is illustrated by a number of examplary studies on the uncertainty of the effective material response of two-dimensional model foams with linear and non-linear elastic material behavior on the cell wall level of structural hierarchy.