The non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transformation into two 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 were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoelectric/piezomagnetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method.The problem is formulated through Fourier transform into 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 are directly expanded as a series of Jacobi polynomials.Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained.The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks.It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials.
