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-infinitecrack propagation in an unbounded lattice and lattice strip are studied.Expressions for the local-to-global energy-release-rate ratios, stressesand strains of the breaking bonds as well as the crack openingdisplacement are derived. Comparative results are obtained forhomogeneous viscoelastic materials, elastic lattices and homogeneouselastic materials. The influences of viscosity, the discrete structure,cell size, strip width and crack speed on the wave/viscous resistancesto crack propagation are revealed. Some asymptotic results related to animportant asymptotic case of large viscosity (on a scale relative to thelattice cell) are shown. Along with dynamic crack propagation, a theoryfor a slow crack in a viscoelastic lattice is derived.