The basic solution of a 3-d rectangular permeable crack in a piezoelectric/piezomagnetic composite material

The solution of a 3-D rectangular permeable crack in a piezoelectric/ piezomagnetic composite material was investigated by using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relations between the electric filed, the magnetic flux field and the stress field near the crack edges were obtained and the effects of the shape of the rectangular crack on the stress, the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed.