On the total electro-mechanical potential energy and energy release rate at the interface crack tips in an initially stressed sandwich plate-strip with piezoelectric face and elastic core layers

An investigation into the values of the total electro-mechanical potential energy and energy release rate (ERR) at the interface crack tips in an initially stressed sandwich plate-strip is carried out for the opening crack mode. It is assumed that the face layers of the considered sandwich plate are made from piezoelectric materials but that the core is made of elastic material, and that this sandwich plate has initial stresses caused by the uniformly distributed normal forces acting on the planes of the two parallel grounded ends of the plate. The plate has two parallel interface cracks symmetrically located with respect to the middle planes and additional uniformly distributed normal opening mechanical forces acting on the cracks' edges. Moreover, the face planes of the face layers and the cracks' edges are unelectroded with vanishing normal electric displacement and are free of electrical charge. The investigations are made by utilizing the three-dimensional linearized theory of electro-elasticity in a plane-strain state within the framework of the piecewise homogeneous body model. The solution to the corresponding boundary value problems are found numerically by employing the finite element method. Numerical results, which are presented and analyzed, illustrate the influences of the geometrical parameters and the initial stresses, as well as the coupling effects between the electro-mechanical fields, on the values of the total electro-mechanical potential energy and of the ERR.