Bounds on the effective tensor and the structural parameters for anisotropic two-phase composite material

This paper is concerned with the estimation of macroscopic properties such as the permittivity or the thermal conductivity of a composite material from the microstructure. A new method of estimating the microstructural parameters, such as the volume fraction of anisotropic two-phase composite material, is derived. The parameters are estimated using information from measurements of the random material or, in the periodic case, from numerical experiments. The method is used to derive new bounds on the effective tensor that incorporates information from measurements of a related parameter. These new bounds are called cross-property bounds. New tight bounds on low-order microstructural parameters are given in the anisotropic case.