Electrical conductivity of fractured materials: Hydrodynamic analogy

The effect of non-conducting extended inclusions (cracks) on the electrical conductivity of a conductive medium at direct current was studied using a two-dimensional model. The additional electrical resistance due to the presence of cracks was calculated using the hydrodynamic analogy between potential flow of an ideal incompressible fluid around solids and electric current flowing around cracks. The dependences of the relative additional electrical resistance of the material on the fracturing coefficient in various limiting cases were determined. Their correctness is confirmed by the results of numerical analysis of the obtained expressions for various fracturing coefficients of the sample for thin and thick samples. The cases of parallel cracks and cracks randomly oriented in different directions were investigated.