Critical Assessment 18: Elastic and thermal properties of porous materials – rigorous bounds and cross-property relations

Abstract

A critical assessment of model relations describing the porosity dependence of elastic properties (Young's modulus) and thermal properties (thermal conductivity) is given. It is shown that there are essentially five types of admissible predictive model relations for the relative Young's modulus and thermal conductivity of isotropic porous materials. The cross-property relations resulting from the complete analogy between the model relations for the elastic moduli and thermal conductivity of isotropic porous materials are reviewed and compared. Finally, it is shown that the fact that relative Young's moduli are not equal to relative thermal conductivities except for materials with translational symmetry, i.e. the mere existence and necessity of non-trivial cross-property relations, proves so-called minimum solid area models to be wrong.