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 eta 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 Delta 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 eta introduces some new twists. More importantly, for large N even at large Delta, the standard two-dimensional elastodynamics approach completely misses the eta-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.
Kessler
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Department of Mathematics, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
Levine
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