Basic solution to four three-dimensional rectangular limited-permeable cracks in transversely isotropic magneto-electro-elastic material

The solution to four three-dimensional rectangular cracks in magneto-electro-elastic material is proposed by using the generalized Almansi's theorem and the Schmidt method under limited-permeable boundary conditions. The problem is formulated through Fourier transform as three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the effects of the electric permittivity, the magnetic permeability of the air inside the crack, the geometric shape of the rectangular crack and the distance among four rectangular cracks on the stress intensity factors, the electric displacement intensity factors and the magnetic flux intensity factors in magneto-electro-elastic material are presented and the magneto-electro-elastic coupling effects are also discussed.