A multi-scale framework for effective elastic properties of porous materials

This paper presents a statistical micromechanics-based multi-scale material modeling framework to predict the effective elastic moduli of porous materials. The present formulation differs from most of the existing theoretical models in that the interaction effects among the pores are directly accounted for by considering the pair-wise interaction and the statistical information of pore distribution is included by applying the ensemble volume averaging process. The theory of average fields is employed to derive the stress and strain concentration factor tensors that relate the local average fields to the global averages. Closed-form and analytical explicit expressions for the effective elastic moduli of porous materials are obtained in terms of the mechanical properties of the matrix material and porosity. The dependence of effective elastic properties on the porosity is investigated. Comparison of our theoretical prediction with the results of the published experimental data and other existing theoretical models is performed to illustrate the predictive capability of the proposed framework for porous materials.