Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack

This paper presents an exact treatment on the problem of an elliptic hole or a crack in a magnetoelectroelastic solid subject to the farfield loadings. First, based on the extended version of Eshelby-Stroh’s formulation, the general solution of an elliptical hole is obtained according to exact boundary conditions at the rim of the hole. Then, when the hole degenerates into a crack, explicit solutions are given for the field intensity factors and electric–magnetic fields inside the crack. It is shown that all the singularities of fields are dependent on the applied mechanical loads, not on the applied electric–magnetic loads. Due to its explicitness, the present solution for a crack can also serve as a benchmark to test the validity of various analysis approaches or assumptions to more complicated crack problems in magnetoelectroelastic media.