Geometrically nonlinear stress–strain behavior of hyperelastic solid foams

The present study is concerned with an effective stress analysis of cellular solids in the finite strain regime. The homogenization of the microstructure is performed by means of a strain energy based RVE-procedure which assumes macroscopic equivalence of a representative volume element for the given microstructure and a similar volume element consisting of the effective medium, if the average strain energy density in both volume elements is equal provided that the deformation gradient with respect to both elements is equal in a volume average sense. Disordered microstructures are considered by means of a randomized periodic model in conjunction with a stochastic approach. The model is applied to an analysis of the effective stress–strain behavior of two-dimensional model foams with periodic and disordered microstructure. Special interest is directed to effects of the geometric nonlinearity.