An electroded electrically and magnetically charged interface crack in a piezoelectric/piezomagnetic bimaterial

Abstract

An interface crack between two semi-infinite piezoelectric/piezomagnetic spaces under the action of remote mechanical loading, magnetic and electric fluxes is considered. The bimaterial is polarized in the direction orthogonal to the crack faces, and all fields are assumed to be independent of the coordinate co-directed with the crack front. The crack faces are covered with mechanically soft electrodes of ferroelectric material having a prescribed electric charge and residual magnetic induction. Special presentations of electromagnetomechanical quantities via sectionally analytic functions are used. “Open” and contact zone interface crack models are considered. In the first case, the formulated problem is reduced to a Hilbert problem and in the second one to a sequence of combined Dirichlet–Riemann and Hilbert boundary value problems. In both cases, the solutions of the mentioned problems are presented in exact analytical form. The well-known phenomenon of the crack-face interpenetration is observed for the “open” model, and the transcendental equation for the contact zone length determination is derived for the contact zone model. For a numerical illustration of the obtained results, the influence of the mechanical loading and the intensity of electric and magnetic fluxes upon the crack opening, mechanical, electric and magnetic fields at the crack region are shown.