A probabilistic approach to the numerical homogenization of irregular solid foams in the finite strain regime

The present study is concerned with the numerical homogenization of hyperelastic two-dimensional model foams with irregular microstructure under large macroscopic deformation. In contrast to the standard procedure of a single analysis of a large-scale representative volume element where the microstructure is determined by means of a Voronoi tesselation or a similar method, the present study proposes a direct probabilistic approach based on the multiple analysis of small-scale representative volume elements with randomized microstructure. Advantage of this method compared to the standard procedures is the possibility of a proper stochastic assessment of the simulation results. Especially, the scatter which has to be expected in the stress-strain response of the effective material becomes accessible in terms of the standard deviation. In a number of parameter studies it is observed that an increasing microstructural disorder results in a decrease of the effective stiffness of cellular solids due to variations in the underlying microstructural mechanisms of deformation. (C) 2004 Elsevier Ltd. All rights reserved.