Exact and fundamental solution for an anti-plane crack vertical to the boundaries of a magnetoelectroelastic strip

In this article, we develop a closed-form solution for a crack in a magnetoelectroelastic strip of finite width, subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stresses, electric and magnetic fields, together with their intensity factors are obtained for the two extreme cases of an impermeable crack and a permeable crack. Solutions for some special cases, such as a center crack, an edge crack, a semi-infinite medium, and an infinite medium, are also obtained in closed-forms. The problem of two symmetric and collinear cracks is also discussed. It is found that the electrically and magnetically permeable conditions on the crack profile are important in obtaining the correct crack tip electromagnetic filed intensity factors. The stress intensity factor, however, does not depend on the crack electromagnetic boundary condition assumptions.