Effect of pore coalescence on the effective conductivity of an isotropic material

The purpose of this work is to evaluate effect of two coalesced pores or insulating inhomo-geneities on the overall conductive properties of an isotropic material. Analytical modeling of the effective properties of materials with microstructures formed by inhomogeneities of non-ellipsoidal shape has not been well developed. The inhomogeneities are typically assumed to be ellipsoids of identical aspect ratios. This unrealistic assumption is largely responsible for insufficient linkage between methods of micromechanics and material science applications. The resistivity contribution tensor gives the extra temperature gradient produced by introduction of the inhomogeneity into a material subjected to otherwise uniform heat flux. The main goal of this work is to obtain an analytical solution for the components of the resistivity contribution tensor of two overlapping pores, in the 2D and 3D frameworks [1, 2].