Effective Conductivities of Thin-Interphase Composites

TL;DR

This paper introduces an efficient method to approximate the effective conductivity of composite materials with thin interphase regions, applicable to various configurations and anisotropies, assuming intermediate interphase conductivities.

Contribution

The paper presents a first-order accurate, computationally efficient approximation method for effective conductivity in composites with thin interphases, accommodating complex geometries and anisotropic phases.

Findings

Method is exact to first order in interphase thickness.

Applicable to multiple interphases and anisotropic conductivities.

Computationally efficient by using reference composite fields.

Abstract

A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the fields need to be computed only in a reference composite in which the interphases have been replaced by perfect interfaces. The results apply whether any two phases of the composite are separated by a single interphase or multiple interphases, whether the conductivities of the composite phases are isotropic or anisotropic, and whether the thickness of an interphase is uniform or varies as a function of position. It is assumed that the conductivities of the interphase materials have intermediate values as opposed to very high or very low conductivities.