Dynamic analysis of an interface crack between magnetoelectroelastic and functionally graded elastic layers under anti-plane mechanical and in-plane electro-magnetic loadings

The dynamic response of an interface crack between magnetoelectroelastic and functionally graded elastic layers under anti-plane shear and in-plane electric and magnetic impacts is investigated by the integral transform method. Fourier and Laplace transforms are applied to reduce the mixed boundary value problem of the interface crack to dual integral equations, which are expressed in terms of a Fredholm integral equation of the second kind. The singular stress, electric displacement and magnetic induction fields near the crack tip are obtained asymptotically, and the stress intensity factors (SIFs), electric displacement intensity factors (EDIFs) and magnetic induction intensity factors (MIIFs) are determined accordingly. Laplace inverse transform is applied to get the field intensities in time domain. Numerical results show how the dynamic SIF is influenced by the magnetoelectric interactions, the material properties, the electric and magnetic loadings, and the geometric size ratios and the functionally graded parameter.