Mode III fracture of a magnetoelectroelastic layer: exact solution and discussion of the crack face electromagnetic boundary conditions

This paper develops a closed-form solution for anti-plane mechanical and in plane electric and magnetic fields in a magnetoelectroelastic layer of finite thickness. Explicit expressions for the stresses, electric fields, and magnetic fields, together with their intensity factors are obtained for the extreme cases for impermeable and permeable cracks. Solutions for some special cases, such as a magnetoelectroelastic layer with infinite thickness, are also obtained. Applicability of the crack face electromagnetic boundary conditions is discussed. It is found that the crack profile is important in obtaining the correct electromagnetic fields and their intensity factors. The stress intensity factor, however, does not depend on the crack face electromagnetic boundary condition assumptions.