Mode I vertical elliptic crack problem of multiferroic composites

Abstract Three-dimensional crack analyses of multiferroic composites with material anisotropy have been challenging due to its mathematical complexity, which limits the further understanding of fracture mechanics in magneto-electro-elasticity. This paper examines a mode I elliptic crack problem in transversely isotropic magneto-electro-elasticity. The crack considered here is embedded on the plane vertical to the isotropic plane of an infinite multiferroic composite. Starting from the point dislocation problem of a half-space, we establish the governing boundary integral equation for this vertical crack problem. Based on the generalized potential theory method, the complete coupling field is obtained in terms of simple integrals and the stress intensity factor is derived as well. The finite element simulation is also performed to validate the present solutions.