Sesqui-power scaling of plateau strength of closed-cell foams

Experimentally obtained elastic and strength properties of closed-cell foams under compressive loading are frequently characterized by power-law scaling with the relative density of the material, i.e. the volume fraction of the solid material phase. Hereby, the so-called plateau strength, which may constitute the most vital material parameter for moderate deformation states, obtained from experiments on samples with different overall porosities, but same matrix material and pore topology often exhibits sesqui-power scaling. In this paper, this porosity-property relation of closed-cell foam is assessed by: (i) specialization of classical schemes from continuum micromechanics for high porosities, with the so-called differential scheme resulting in sesqui-power scaling of the effective strength; (ii) applying the closed form solution for plastic buckling of a thin spherical shell within the scopes of a unit-cell think-model for closed-cell foams, also giving the power-law scaling exponent as 3/2.