A Hyperelastic Model for Soft Polymer Foam Including Micromechanics of Porosity

This paper proposes a new isotropic hyperelastic model for polymer foam, which explicitly models the micromechanical influence of changes in porosity. The foam is treated as a matrix of compressible solid material with evacuated pores that cause soft response for low pressures. In its general form, the strain energy of the foam depends on the strain energy of the solid material and on the porosity, which is taken to be a function of the total dilatation. This function adds only two material constants. One is the stress free porosity and the other controls the magnitude of the low pressure response of the foam. In contrast with other formulations, the proposed model naturally transitions to the response of the solid as the porosity approaches zero in hydrostatic compression.