Relation between Effective Conductivity and Susceptibility of Two -- Component Rhombic Checkerboard

Abstract

The heterogeneity of composite leads to the extra charge concentration at the boundaries of different phases that results essentially nonzero effective electric susceptability. The relation between tensors of effective electric susceptability $\hat\chi_{ef}$ and effective conductivity $\hat\sigma_{ef}$ of the infinite two--dimensional two--component regular composite with rhombic cells structure has been established. The degrees of electric field singularity at corner points of cells are found by constructing the integral equation for the effective conductivity problem. The limits of weak and strong contrast of partial conductivities $\sigma_1,\sigma_2$ are considered. The results are valid for thin films and cylindrical samples.