Elliptic crack in transversely isotropic magneto-electro-elasticity under shear loading

In this paper, a novel elliptical crack problem in magneto-electro-elasticity is studied. Unlike conventional crack problems in which the cracks are usually assumed to be embedded on a horizontal plane parallel to the isotropic plane of a transversely isotropic material, this paper studies a vertical crack with its surface perpendicular to the isotropic plane. The crack is under the action of uniformly distributed shear loads applied on the crack surfaces. The boundary integro-differential equation is derived by the generalized potential theory method. For an elliptical crack, the complete and closed-form coupling field is presented in the integral form, for the first time. Some significant quantities in fracture mechanics are obtained explicitly, in terms of elementary functions. Furthermore, numerical simulations are performed by finite element method to discuss the validity of the present analytical solutions.