Effective conductivities of thin-interphase composites

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efficient in the sense the fields need to be computed only in a reference composite in which the interphases have been replaced by perfect interfaces.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.