2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16062We extend the Slepyan solution of the problem of a steady-state crack in an infinite ideally brittle lattice model to include dissipation in the form of Kelvin viscosity. As a demonstration of this technique, based on the Wiener-Hopf method, we apply the method to mode III cracks in a square lattice. We use this solution to find the critical velocity at which the steady-state solution becomes inconsistent due to additional bond-breaking; this point signaling the onset of complex dynamical behavior.14 pages, 6 figures, RevTeX4, Replaced incorrect Fig. 1Materials Sciencetext