Green’s functions and extended displacement discontinuity method for interfacial cracks in three-dimensional transversely isotropic magneto-electro-elastic bi-materials

In this paper, we derive the Green’s functions of constant extended interfacial displacement discontinuities within a rectangular element and of point extended interfacial displacement discontinuities in three-dimensional transversely isotropic magneto-electro-elastic (MEE) bi-materials. The derived Green’s functions along with the extended displacement discontinuity method are applied to analyze the electrically and magnetically impermeable interfacial cracks in the three-dimensional MEE bi-materials. To deal with the oscillatory singularities at the crack front, the Dirac delta function in the Green’s functions is replaced by the Gaussian distribution function, and correspondingly, the unit Heaviside function is approximated by the Error function. Numerical study illustrates the effect of the ε parameter in the Gaussian distribution function on the J-integral. The stress intensity factors, electric displacement intensity factor, and magnetic induction intensity factor are expressed in terms of the extended displacement discontinuities. The influence of different MEE material mismatches as well as different extended loadings (uniformly or non-uniformly distributed on the crack face) on the fracture parameters is investigated. Different rectangular crack sizes are also considered in the numerical simulation.