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.