Electrically Plane and Mechanically Antiplane Problem for an Inclusion with Stepwise Rigidity Between Piezoelectric Materials

Abstract

An electrically insulated inclusion at the interface of two piezoelectric semi-infinite spaces under the action of antiplane mechanical and in-plane electric loadings is analyzed. One zone of the inclusion is absolutely rigid while the other part is mechanically soft. This problem is important for practical applications, but it has not been solved earlier at least in an analytical way. The presentations of all electro-mechanical quantities via sectionally-analytic vector-functions are obtained. With use of these presentations, the combined Dirichlet-Riemann boundary value problem is formulated and an exact analytical solution of this problem is found. On the base of this solution, the closed form analytical expressions for the required electro-mechanical quantities along the interface are derived. Particularly the stress jump along the mechanically rigid part of the inclusion is found and additionally the variation of this stress along its upper face is also given. The values of electromechanical quantities along the corresponding parts of the material interface are presented graphically. Singular points of the shear stress, strain and also the electric displacement and field are found and the corresponding intensity factors are determined. The dependence of the stress intensity factor on the intensity of the electric displacement and the relation of the rigid and soft zone lengths is investigated.