A dielectric breakdown model for an electrode along an interface between two piezoelectric materials

Abstract

A plane strain problem for an interface electrically charged thin electrode in a bimaterial piezoelectric space is considered. Remote in-plane mechanical loading and an electrical field parallel to the electrode faces are applied. The known solution of this problem demonstrates the electromechanical field singularities at the electrode tips. To remove these singularities the dielectric breakdown model is applied. Using the presentations of electromechanical quantities via sectional analytic functions the Riemann-Hilbert problem with discontinuous right side is formulated and solved exactly. The dielectric breakdown zone lengths are found from the electric field finiteness at the end points of these zones. It is shown that this length depends on the external electric field and the electrode net charge. The variations of electromechanical characteristics along the electrode and its continuation are presented in graphical form. Particular cases of an uncharged electrode and homogeneous material are considered and compared with previously obtained results. A verification of the obtained solutions by means of the ABAQUS code is carried out and good agreement of analytical and numerical results is revealed.