Three-dimensional exact magneto-electro-elastic field in an infinite transversely isotropic space with an elliptical crack under uniform loads: Shear mode

Abstract This paper studies an elliptical planar crack embedded in an infinite transversely isotropic medium in the framework of magneto-electro-elasticity. The crack is assumed to be subjected to uniformly distributed shear loads, which are anti-symmetrical with respect to the crack plane. The boundary integral equation is established via the general solution in conjunction with the generalized method of potential theory. Exact and complete field variables are obtained in terms of elliptical functions. Important parameters in fracture mechanics, e.g., the crack slip displacement, the shear stress at the crack front, and the corresponding stress intensity factor, are explicitly derived. The corresponding solutions, in the context of piezoelectricity, piezomagnetism and pure elasticity are also presented, as a byproduct of the present work. The present closed-form analytical solutions may serve as benchmarks for future simplified and numerical studies.