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.