Porosity dependence of mechanical properties of solid materials

The generalized means are used as a simple but elegant mixture rule for providing a unified description of the physical properties of polyphase composites in terms of component properties, volume fractions, and microstructures. This formula is named as the generalized mixture rule (GMR). Taking porous materials as a special class of two-phase composites in which pores are dispersed within a solid framework, the GMR yields a rigorous expression for the porosity dependence of the mechanical properties. Although the GMR is purely mathematical in origin, its connection to the existing theories and its consistence with extensive experimental data suggests that it should have some physical validity as a hypothesis or at least a very handy tool for a general description of the mechanical properties of multiphase materials including porous solids.