Conductivity of a two-dimensional model of a structurally anisotropic composite with a system of scratches

The conductivity of a two-dimensional model of a structurally anisotropic composite, an isotropic matrix with nonconducting inclusions in the form of parallel scratches, is considered. The centers of the scratches are randomly distributed over the (x, y) plane. An approximate method is applied to derive an expression for the effective conductivity tensor, which satisfactorily describes of the electric conductivity of the model over a wide range of concentrations.