Steady-state cracks in viscoelastic lattice models

We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity η allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement Δ and the number of transverse rows N. At any N, the continuum theory misses the lattice-trapping phenomenon; this is well known, but the introduction of η introduces some new twists. More importantly, for large N even at large Δ, the standard two-dimensional elastodynamics approach completely misses the η-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.