Electrical conductivity of a two-dimensional model for a composite material with structural anisotropy

The electrical conductivity of a structurally anisotropic two-dimensional model for a composite material is considered. The model represents an isotropic matrix with a system of nonconducting inclusions in the form of mutually perpendicular scratches of various lengths. The centers of the scratches are chaotically distributed in plane $(x, y)$. The approximate effective medium method is used to derive an expression for effective conductivity tensor $\hat{\sigma}_e$ that satisfactorily describes the electrical conductivity of this model over a wide concentration range. The model conductivity in the critical region is considered in terms of the similarity hypothesis.