The energetics of heterogeneous deformation in open-cell solid foams

Compressed open-cell solid foams frequently exhibit spatially heterogeneous distributions of local stretch. The theoretical aspects of this deformation habit have not been clearly elucidated. Here we propose a simple nonlinear model aimed at illustrating the most salient features of the micromechanics of uniaxially stretched solid foams. Then we study the energetics of the model to show that the stretch heterogeneity observed in experiments stems from the lack of convexity of the governing energy functional, which favours two characteristic values of local stretch. These characteristic values are independent of the applied overall stretch and define two configurational phases of the foam. The predicted stretch distributions correspond to stratified mixtures of the phases; stretching occurs in the form of a phase transformation, by growth of one of the phases at the expense of the other. We also compare the predicted mechanical response with experimental data for a series of foams of different densities and discuss the analogy between the stretching of foams and the liquefaction of van der Waals gases. Lastly, we perform displacement field measurements using the digital image correlation technique and find the results to be in agreement with our predictions.