Displacement discontinuity analysis of a nonlinear interfacial crack in three-dimensional transversely isotropic magneto-electro-elastic bi-materials

The displacement discontinuity method is introduced and extended to study the electric and magnetic nonlinear effect of an interfacial crack in three-dimensional magneto-electro-elastic bi-materials under combined loadings. Green’s functions due to uniformly distributed extended displacement discontinuities over a ring element are derived via the extended displacement discontinuity integro-differential equation method. The electric−magnetic polarization saturation model is adopted for the electric and magnetic nonlinearities at the vicinity of the crack front where the perfect electric displacement and magnetic induction saturations are assumed. The final formulation is discretized as a system of linear equations and an iterative approach is introduced to solve the unknown sizes of the two saturation zones by requiring that the electric displacement and magnetic induction intensity factors vanish at ends of their corresponding zones. The effect of the electric and magnetic fields on the saturation zones and the influence of the saturation zones on the stress intensity factor are illustrated with numerical examples.