Steady-State Cracks in Viscoelastic Lattice Models

Abstract

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.