Refined polarization approximations for conductivity of isotropic composites

The polarization approximations for the effective conductivity of isotropic multicomponent materials, constructed recently from a variational approach, are refined to include more information about the composites, if available, to improve the accuracy of the scheme. The variable reference parameter of the approximation may be determined from an asymptotic solution (in series) for the effective conductivity of a particular composite at small volume proportions of the inhomogeneities, which contains more information about the composite than the dilute solution result. Practically, the variable parameter can be calibrated through available reference numerical or experimental macroscopic conductivities of the composite at finite volume proportions of the component materials, or from a combination of those references. By construction, the approximations satisfy Hashin-Shtrikman bounds, at least, over the range of the component's volume proportions within the extreme reference points. Illustrations of applications are provided in a number of examples involving numerical and/or experimental data, which shows the flexibility and usefulness of the approach.