Steady-state mode III cracks in a viscoelastic lattice model

TL;DR

This paper extends a lattice model of steady-state mode III cracks by incorporating Kelvin viscosity, using Wiener-Hopf method to analyze critical velocities and the onset of complex crack dynamics.

Contribution

It introduces a viscous extension to the lattice crack model and applies Wiener-Hopf method to analyze crack behavior with dissipation.

Findings

Identifies critical velocity where steady-state breaks down

Demonstrates the effect of Kelvin viscosity on crack dynamics

Provides a framework for analyzing dissipative lattice cracks

Abstract

We extend the Slepyan solution of the problem of a steady-state crack in an infinite ideally brittle lattice model to include dissipation in the form of Kelvin viscosity. As a demonstration of this technique, based on the Wiener-Hopf method, we apply the method to mode III cracks in a square lattice. We use this solution to find the critical velocity at which the steady-state solution becomes inconsistent due to additional bond-breaking; this point signaling the onset of complex dynamical behavior.