Exact solution for an elliptical cavity or crack in a reinforced magnetoelectroelastic material under anti-plane shear

An exact solution for an elliptical cavity embedded in a reinforced, magnetoelectroelastic material under anti-plane shear and in-plane electric and magnetic loading is provided in this paper. Explicit forms of the mechanical, electric and magnetic fields in the matrix, the reinforcement layer and the elliptical cavity are obtained by means of the method of complex potentials. The electromagnetic fields inside the elliptical cavity have been taken into consideration, and explicit solutions for a mode III crack, either impermeable or permeable, are obtained when the elliptical cavity is reduced to a crack. The change of energy due to the presence of the cavity and reinforcement layer has been derived. Some special cases, such as the elliptical cavity problem and crack problem are discussed in detail to illustrate the validity and versatility of the current formulation.