Relation between Effective Conductivity and Susceptability of Two – Component Rhombic Checkerboard

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 χ̂ef and effective conductivity σ̂ef 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 σ1, σ2 are considered. The results are valid for thin films and cylindrical samples.