Steady-State Cracks in Viscoelastic Lattice Models II

TL;DR

This paper analytically solves the steady-state Mode III crack problem in a viscoelastic lattice, analyzing effects of viscosity, lattice width, and bifurcation behavior, and identifying the process zone where continuum theory fails.

Contribution

It provides an exact analytical solution for a viscoelastic lattice crack model, including effects of viscosity and lattice geometry, extending previous continuum approaches.

Findings

Analytic solution for steady-state crack in viscoelastic lattice.

Identification of the process zone size where continuum theory breaks down.

Analysis of bifurcation structure at small velocities.

Abstract

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.