NUMERICAL INSTABILITY AT THE EDGE OF A DYNAMIC FRACTURE

Abstract

Numerical solutions by finite-difference techniques to problems of dynamical fracture growth exhibit oscillations with large amplitudes near the edges of the fractures that are caused by the stepwise advance of the edge of the crack across the computational lattice. In their turn, the oscillations cause anomalously large velocities of crack growth and slightly larger than expected velocities of slip in the interior of the crack. These undesirable consequences of computation of dynamical fractures on a discrete lattice can be minimized by the insertion of dissipation in the elastic properties of the system having about 1/3 of the value for critical damping at the lattice cutoff frequency.