Electrical conductivity of a two-dimensional model for a structurally anisotropic composite

The electrical conductivity of a two-dimensional structurally anisotropic model for a composite is considered. The model represents an isotropic matrix with a system of nonconducting inclusions in the form of infinitely thin straight line segments (scratches). The scratches make an angle θ or −θ with a preferred axis (for definiteness, axis y) at the same probability, and their centers are chaotically distributed. An approximate effective medium method is used to obtain a general expression for the effective conductivity tensor $ \hat \sigma _e $ \hat \sigma _e of this model that is valid over a wide concentration range. In this approximation, both components of tensor are $ \hat \sigma _e $ \hat \sigma _e shown to vanish at the same percolation threshold, which is expressed explicitly. The conductivity of the model in a critical region is considered in terms of the similarity hypothesis.