Investigation of the scattering of harmonic elastic antiplane shear waves by a finite crack using the non-local theory

In this paper, the scattering of harmonic antiplane shear waves by a finite crack is studied using the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual integral equations is solved using the Schmidt method instead of the first or the second integral equation method. Contrary to the classical elasticity solution, it is found that no stress singularity is presented 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.