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 sites 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.Comment: 27 pages, 8 figure