Assessment of material uncertainties in solid foams based on local homogenization procedures

Abstract

The present study is concerned with a numerical prediction and assessment of uncertainties in the macroscopic material properties of solid foams. The material properties are determined by means of a homogenization analysis considering a large scale representative volume element. The microstructure for the representative volume element is determined randomly using a Voronoï tesselation in Laguerre geometry with prescribed cell size distribution. For assessment of the scatter in the effective material response, the homogenization scheme is applied to subsets of the large scale representative volume element. By this means, an interrelation between the local microstructural characteristics and the local mesoscopic material response is established. In a first approach, the individual cells of the foam microstructure are employed as testing volume elements. As an alternative, a moving window technique is applied. The sets of homogenization results obtained by both approaches are evaluated by stochastic methods. For the local effective properties, a distinct scatter is observed. The results in both cases reveal that the local porosity is the most important influence parameter. For the microstructures investigated, only weak local correlations of the effective stiffnesses with a rapid spatial decay of the correlation is observed.