Finite size effects on a cracked magnetoelectroelastic layer sandwiched between two elastic layers

Abstract

The crack problem of a magnetoelectroelastic layer of finite size sandwiched between two elastic layers under anti-plane shear and in-plane electric and magnetic loads is considered for impermeable and permeable crack surface conditions, respectively. Fourier transforms and Fourier sine series are used to reduce the mixed boundary value problem of the crack to dual integral equations, which are expressed in terms of Fredholm integral equations of the second kind. The stress field, electric field and magnetic field near the crack tip are obtained asymptotically, and the corresponding field intensity factors for impermeable and permeable cracks are determined. Numerical results show that the stress intensity factors, the electric displacement intensity factors and the magnetic induction intensity factors are influenced by the electric and magnetic loadings and the material properties. The finite size effects on the fracture behavior of the composite structure are investigated.