A system of interface cracks with different electric conditions at their faces in a magnetoelectroelastic bimaterial

A plane strain problem for a set of collinear cracks along the interface between dissimilar magnetoelectroelastic materials is considered. The number of cracks, their location, and lengths can be arbitrary. Remote mixed-mode mechanical loading, electric, and magnetic induction are prescribed at infinity. Two cases of magnetic and electric conditions at the crack faces are considered. First case assumes that the crack is electrically and magnetically permeable, and in the second case, the crack is assumed electrically permeable and magnetically impermeable. Using the presentations of mechanical, electric, and magnetic quantities via sectionally analytic vector functions, problems of linear relationship are formulated and solved analytically. The analytical expressions for mechanical, electric, and magnetic quantities at different parts of the material interface as well as their asymptotic expressions at the crack tips are obtained in the closed form. Using these expressions together with the crack closer integral, the energy release rates near right and left tips of the cracks are obtained in analytical form. The graphs of stresses and magnetic induction between cracks and also crack faces normal displacement jumps are presented for both crack models, different crack locations, their lengths, mechanical, and magnetic loading. The corresponding energy release rates are also found. These parameters are significant for assessing failure mechanisms and enhancing the reliability of magnetoelectroelastic composites during their operation.