Analysis of interfacial crack problems in three-dimensional magneto-electro-elastic bimaterials using hypersingular integral-differential equation method

摘要

A planar interface crack in a three dimensional transversely isotropic magneto-electro-elastic bimaterials under magneto-electro-elastic coupled loads is analyzed. Using the concept of finite-part integral and boundary integral method, the interface crack problem is reduced to solve a set of hypersingular integro-differential equations, where the unknown functions are the discontinuities of the extended displacements of the crack surface. The singularity of the unknowns at the crack front is analyzed by the main-part analysis method of the hypersingular integro-differential equations. Comparing with the interface crack problems in elastic isotropic bimaterials, it is shown that the extended intensity factors for magneto-electro-elastic bimaterials can be obtained from those for elastic isotropic bimaterials. Based on the exact analytical solutions of the singular extended stresses and extended displacements near the crack front, a numerical method for the hypersingular integro-differential equations is proposed by the finite-part integral method, where the extended displacement discontinuities are approximated by the product of basic density functions and polynomials. Finally, the distribution of extended stress intensity factors at the interface crack surface is calculated, and the results are presented toward demonstrating the applicability of the proposed method.