Non-local theory solution of a limited-permeable mode-I crack in a piezoelectric/piezomagnetic material plane

The non-local theory solution of a limited-permeable mode-I crack in a piezoelectric/piezomagnetic media was given by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transform into two 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. Numerical examples were provided to show the effects of the lattice parameter, the crack length, the electric permittivity, and the magnetic permeability of the air inside the crack on the stress field, the electric displacement field, and the magnetic field near the crack tip. Different from the classical solution that the present solution exhibits no stress, electric displacement, and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic media. The non-local theory solution of a limited-permeable mode-I crack in a piezoelectric/piezomagnetic media was given by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve these 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 lattice parameter, the crack length, the electric permittivity, and the magnetic permeability of the air inside the crack on the stress field, the electric displacement field, and the magnetic field near the crack tip. Different from the classical solution that the present solution exhibits no stress, electric displacement, and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic media.