An interaction of electrically conductive and electrically permeable collinear cracks in the interface of piezoelectric materials

An interaction of electrically conductive and electrically permeable collinear cracks along an interface between two piezoelectric materials under the action of anti-plane mechanical loading and in-plane electric field is considered. It is assumed that the electric field is parallel to the crack faces and the materials polarization is co-directed with the crack fronts. Using the presentations of all required electromechanical quantities via sectionally analytic vector-function, a combined Dirichlet-Riemann boundary value problem is formulated. A closed-form analytical solution of this problem is presented for any distances between the cracks, any cracks lengths and any external loadings of the above-mentioned type. Analytical expressions for the shear stress, the electric field and their intensity factors as well as for the mechanical and electric displacement jumps are presented. The energy release rates are found for all crack tips, and their variation with respect to the external loading and the distance between the cracks is demonstrated.