Non-local theory solution to a rectangular crack in a 3D infinite orthotropic elastic medium

The non-local theory solution to a rectangular crack in a 3D infinite orthotropic elastic medium is investigated by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem is formulated through the double Fourier transform into 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. Numerical examples are provided to illustrate the effects of the geometric shape of the rectangular crack and the lattice parameter on the stress fields near the crack edges. Different from the classical solutions, the present solutions exhibit no stress singularity along the rectangular crack edges in an orthotropic elastic medium. Thus, this allows us to use the maximum stress as a fracture criterion.