Analysis of dynamic failure of the discrete chain structure with non-local interactions

In the present work, the steady-state crack propagation in a chain of oscillators with non-local interactions is considered. The interactions are modelled as linear springs, while the crack is presented by the absence of extra springs. The problem is reduced to the Wiener-Hopf type, and solution is presented in terms of the inverse Fourier transform. It is shown that the non-local interactions may change the structure of the solution well known from the classical local interactions formulation. In particular, it may change the range of the region of stable crack motion. The conclusions of the analysis are supported by numerical results. Namely, the observed phenomenon is partially clarified by evaluation of the structure profiles on the crack line ahead.