Polarization approximations for macroscopic conductivity of isotropic multicomponent materials

Hashin-Shtrikman-type polarization trial fields, constructed earlier by us to derive bounds on the effective conductivity of isotropic multicomponent materials, are used to derive polarization approximations for the macroscopic transport property of the d-dimensional composites (d=2 or 3). The approximation contains a free parameter, which should be determined from a reference model at certain volume proportions of the component materials theoretically, numerically, or experimentally. Once the appropriate reference parameter had been chosen, the approximation would obey Hashin-Shtrikman bounds over all the ranges of volume proportions of the component materials. The approximation is expected to do best near the component-volume-proportion reference point. Numerous examples are given to illustrate the usefulness of the approach.