Scattering of harmonic anti-plane shear waves by an interface crack in magneto-electro-elastic composites

The dynamic behavior of an interface crack in magneto-electro-elastic composites under harmonic elastic anti-plane shear waves is investigated for the permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable was the jump of the displacements across the crack surfaces. To solve the dual integral equations, the jump of the displacements across the crack surface was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effect of the length of the crack, the wave velocity and the circular frequency of the incident wave on the stress, the electric displacement and the magnetic flux intensity factors of the crack. From the results, it can be obtained that the singular stresses in piezoelectric / piezomagnetic materials carry the same forms as those in a general elastic material for anti-plane shear problem.