Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

Abstract

Dislocation‐based analysis of cracked magnetoelectroelastic solid under remotely uniform anti‐plane mechanical with in‐plane electromagnetic loading is presented. The solution to the generalized dislocation including screw dislocation and electric and magnetic jumps within an incompatible framework are reviewed from the literature. In order to model the system of multiple cracks in the solid, the dislocations are distributed along the crack faces. Then the densities of the dislocations are evaluated by applying the crack‐face boundary conditions. Both permeable and impermeable conditions are discussed. The entire field components including shear stress, electric displacements and magnetic inductions are determined for the cracked material, which is an advantage comparing to the methods which only provide crack tip field components. The field intensity factors are also formulated for both permeable and impermeable conditions. Finally examples including horizontal crack, inclined crack and multiple cracks are studied.