A cascade continuum micromechanics model for the effective elastic properties of porous materials

The elastic properties of porous materials with a disordered pore structure are estimated using the mean-field Eshelby homogenization scheme together with the principle of recurrence to generate a cascade of effective microstructures as a function of the porosity and the cascade level n. Starting with the Hashin–Shtrikman upper bound for porous materials, the proposed cascade micromechanics model generates a hierarchy of micro-structures which evolve from an initial configuration of a porous material with spherical pores embedded within an elastic solid phase consistent with the Mori–Tanaka matrix inclusion morphology to a porous material characterized by a hierarchic distribution of spherical elastic grains. The model is explicit and allows for an easy computational implementation. It predicts physically consistent threshold porosities, characteristic for the specific morphology of the porous material under consideration, beyond which the material loses its stiffness. The validity of the cascade micromechanics model is evaluated against experimental data for various materials ranging from foam to ceramics with different pore structures.