Microgeometry of random composites and porous media

Abstract

For practical applications of variational bounds to the effective properties of composite materials, the information available is often not that required by the formulas for the optimal bounds. It is therefore important to determine what can be said rigorously about various unknown material properties when some other properties are known. The key quantities to be analyzed are the parameters i and j depending on the microgeometry through integrals of the three-point correlation functions. The physical significance of these parameters for two-phase composites and porous media is elucidated here by examining the various relationships between them and material properties. The bounds on conductivity due to Beran and the bounds on elastic constants due to Beran and Molyneux and to McCoy, as well as those of Milton and Phan-Thien, are considered. For the special case of porous media, the formulas simplify greatly and the resulting analytical relationships between transport properties and geom...