Radially transverse isotropic inclusions in isotropic conductive media: Local fields, effective properties, neutral inclusions

Abstract

Spherical radially transverse isotropic heterogeneous inclusions in homogeneous isotropic conductive host media are considered. The volume integral equation for the field in the medium with an isolated inclusion subjected to a constant external field is solved using Mellin-transform technique. The method allows revealing tensor structure of the solution with precision to one scalar function of radial coordinate. Differential equation for this function arises in the process of realization of the method. For multilayered radially transverse isotropic inclusions, an efficient algorithm of solution is presented. Neutral inclusions that do not disturb constant external fields in the host medium are considered. For neutral inclusions, relations between the conductivity coefficients of the inclusion and the host medium are indicated. It is shown that homogeneous inclusions with a layer of other material at the inclusion interface can be neutral (invisible for external observers). For neutral inclusions, thin boundary layers can be changed with specific boundary conditions at the inclusion interface (singular models of thin layers). Parameters of the singular models are indicated in terms of conductivity coefficients of the inclusion, layer, and host medium. The effective field method is used for calculation of the effective conductivity of homogeneous isotropic media containing random sets of radially transverse isotropic inclusions. Influence of volume fractions and conductivity coefficients of the inclusions on the effective conductivity of the composite is studied.