Investigation of the scattering of harmonic elastic shear waves by two collinear symmetric cracks using the non-local theory

In this paper, the scattering of harmonic shear waves by two collinear symmetric cracks is studied using the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then, a set of triple integral equations is solved using a new method, namely Schmidt's method. This method is simple and convenient for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length.