Strain-energy based homogenisation of twoand three-dimensional hyperelastic solid foams

A possible classification of cellular solids can be made based on the dimension into honeycombs and foams. In numerical simulations 2D models that are employed primarily to study honeycombs can also be used to model open-cell foams. Thereby, a loss of information regarding the 3D connectivity of the microstructure is involved. To answer the question how the missing third dimension in 2D models affects the overall properties, spatially periodic 2D and 3D model foams are adopted. From the point of homogenisation, a strain-energy based scheme is used for adequately determining the effective mechanical properties at large strains. The key idea behind this method is to use directly the equivalence condition between the meso-strain energy and the macro-strain energy. In a first step a representative volume element with the given microstructure and a corresponding volume element containing the effective medium are subjected to equivalent states of deformation. Subsequently, the macroscopic stress-strain relationships are determined by volume-averaging of the stored strain energy. The results of some fundamental loading cases indicate that both model foams represent the deformation characteristics of hyperelastic solid foams like localized bending and elastic buckling. In addition, the development of anisotropy due to microstructural changes at large strains can be traced with both model foams. Nevertheless, the different cell morphology affects the stress-strain curves in a quantitative manner