Dynamic fracture of a rectangular limited-permeable crack in magneto-electro-elastic media under a time-harmonic elastic P-wave

The dynamic behavior of a rectangular limited-permeable crack deeply embedded in transversely isotropic magneto-electro-elastic media was investigated under an incident harmonic stress wave using the generalized Almansi’s theorem and the Schmidt method. With the help of the Fourier transform, this problem was formulated into three pairs of dual integral equations with the jumps in displacement across the crack surfaces as the unknown variables. By directly expanding the jumps in displacement across the crack surfaces into a series of Jacobi polynomials, the solution to the dual integral equations was derived. Finally, the dynamic response of a rectangular crack under a harmonic wave was analyzed, and the effects of the electric permittivity and the magnetic permeability of air inside the crack, the geometric shape of the rectangular crack and the characteristics of the harmonic wave on the stress, the electric displacement and the magnetic flux intensity factors in magneto-electro-elastic media were concluded.