Closed form solution for a line inclusion in magnetoelectroelastic media

This paper studies the problem of a line inclusion in a medium possessing coupled piezoelectric, piezomagnetic and magnetoelectric effects. Based on the extended Stroh formalism, the general two-dimensional solutions to the magnetoelectroelastic problem are obtained, involving five analytic functions of different variables. The magnetic, electric and elastic fields around the inclusion are given. Expressions of the stresses, electric field and magnetic field in the vicinity of the inclusion tip are derived and the field intensity factors are provided. The energy release rate is written in terms of those field intensity factors. Solutions for some special cases, including the electrically and/or magnetically insulated/conductive inclusions/cracks, are also established. Explicit algebraic results are given for a special case of an anti-plane crack in a magnetoelectroelastic medium.