A Lattice Model for Viscoelastic Fracture

A plane, periodic, square-cell lattice is considered, consisting of point particles connected by mass-less viscoelastic bonds. Homogeneous and inhomogeneous problems for steady-state semi-infinite crack propagation in an unbounded lattice and lattice strip are studied. Expressions for the local-to-global energy-release-rate ratios, stresses and strains of the breaking bonds as well as the crack opening displacement are derived. Comparative results are obtained for homogeneous viscoelastic materials, elastic lattices and homogeneous elastic materials. The influences of viscosity, the discrete structure, cell size, strip width and crack speed on the wave/viscous resistances to crack propagation are revealed. Some asymptotic results related to an important asymptotic case of large viscosity (on a scale relative to the lattice cell) are shown. Along with dynamic crack propagation, a theory for a slow crack in a viscoelastic lattice is derived.