Effect of porosity and pore size distribution on elastic modulus of foams

In this study, we investigate the impact of pore distribution and size on the mechanical response of elastic porous materials. Two-dimensional porous media with convex porosity are considered (e.g., foams and sponges). These structures are numerically generated by subtracting randomly dispersed circular holes from a solid square domain. The in-plane position vector of pore centers is given by a uniform probability density function (PDF). The pore diameters are, instead, drawn from a non-uniform two-parameter continuous probability distribution. The influence of the void ratio, i.e., the volume fraction of voids, and the parameters of the diameter PDF are studied over a wide range of values, including the percolation threshold, where the effective elastic modulus of the material abruptly drops to zero. This transition takes place at a critical value of the void ratio, which turns out to be unaffected by the parameters of the pore size distribution. Our results demonstrate that the elastic response of these structures is primarily governed by the void ratio, with the correlation length playing a secondary role. While the pore size distribution may affect the correlation length, it has a minimal impact on the foam's overall behavior.