Micro-statistical modeling of an imperfect interface in a piezoelectric bimaterial under inplane static deformations

A micro-statistical model is proposed for investigating the effective properties of a micro-damaged interface between a piezoelectric layer and a piezoelectric half-space under inplane electroelastostatic deformations. The interface is modeled as damaged by periodic arrays of micro-cracks. The lengths and the positions of the micro-cracks on a period interval of the interface are randomly generated. The conditions on the interfacial micro-cracks are formulated in terms of hypersingular integro-differential equations with the displacement and electrical potential jumps across the interface being unknown functions to be determined. To gain new useful physical insights into the behaviors of the imperfect interface, the influences of the material constants, the width of the layer and the crack densities of the interface on the effective properties of the interface are examined in details.