  In the present work the steady-state crack propagation in a chain of
oscillators with non-local interactions is considered. The interactions are
modeled 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 inverse Fourier transform. It is shown that the non-local
interactions may change the structure of the problem 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.
