A MODE-III CRACK WITH SURFACE EFFECT IN A MAGNETOELECTROELASTIC MEDIUM

In this paper, the contribution of surface effect to the anti-plane deformation of a magnetoelectroelastic medium weakened by a crack is investigated. The surface magnetoelectroelasticity is incorporated by using the extended surface/interface model of Gurtin and Murdoch. The mixed boundary value problem of the mode-III crack is formulated by using a continuous distribution of screw dislocations and the dislocations of electric potential and magnetic potential on the crack, and the problem is finally reduced to solving a system of coupled Cauchy singular integro-differential equations, which can be numerically solved by the decoupling and collocation methods. The results show that the stresses, eldctric displacements and magnetic induction near the crack tips exhibit the logarithmic singularity when the surface effect is considered. When there is no surface effect on the crack face, the classical square-root singularity of the near crack-tip fields can be observed.
EXTENDED ABSTRACT