A simple explicit homogenization solution for the macroscopic elastic response of isotropic porous elastomers

An approximate homogenization solution is put forth for the effective stored-energy function describing the macroscopic elastic response of isotropic porous elastomers comprised of incompressible non-Gaussian elastomers embedding equiaxed closed-cell vacuous pores. In spite of its generality, the solution — which is constructed in two successive steps by making use first of an iterative technique and then of a nonlinear comparison medium method — is fully explicit and remarkably simple. Its key theoretical and practical features are discussed in detail and its accuracy is demonstrated by means of direct comparisons with novel computational solutions for porous elastomers with four classes of physically relevant isotropic microstructures wherein the underlying pores are: (i) infinitely polydisperse in size and of abstract shape, (ii) finitely polydisperse in size and spherical in shape, (iii) monodisperse in size and spherical in shape, and (iv) monodisperse in size and of oblate spheroidal shape.