Stress field near the crack tip in nonlocal anisotropic elasticity

In this paper, the effect of the lattice parameter of the anisotropic materials on the stress field subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. The solutions can be obtained by means of the Schmidt method. This method is simple and convenient for solving such problem. Simultaneously, a closed form solution for the same problem is also given by the classical theory. Contrary to the classical solution, it is found that no stress singularity presents at the crack tip, i.e., the stress field near the crack tips is finite. The magnitude of the finite stress field not only depends on the crack length but also on the lattice parameter of the materials.