Estimating macroscopic conductivity of randomly elliptic inclusion model with imperfect interfaces

Abstract

The paper introduces some solutions for computing the effective conductivity of randomly elliptic inclusion with imperfect interfaces in two-dimensional space. Based on the coated-ellipse inclusion model and the polarization approximation, one can determine the effective conductivity of the ellipse inclusions with the approximation for lowly conducting imperfect interface (ALI) and the approximation for highly conducting imperfect interface (AHI). Some solutions, including the equivalent inclusion approximations (ALI and AHI), differential approximations (DAs), Hamilton–Crosser approximations (HAs), and fast Fourier transformation (FFT) method will be applied to determine the effective conductivity of the randomly ellipse model with AHI and ALI in two-dimensional space. The ALI and AHI results agree well with DA, HA, and FFT results showing the effectiveness of the methods.