Noncausality of numerical models of dynamic fracture growth

Discretization of the wave operator for purposes of solving problems in the dynamics of crack growth numerically, introduces noncausality associated with the nonlinearity of the fracture criterion at the edge of the crack, i.e. with an imperfect formulation of the fracture criterion in the discretized case. The noncausality can be attributed to jumps from one inertial coordinate system to another as successive particles at the edge of a digitized crack are triggered into motion. It is shown that there is an equivalent explanation in terms of the incompatibility of the short-range edge conditions and the long-range correlations of slip on the crack in the discretized case. The noncausal effects can lead to supersonic crack growth, and in some cases to infinite crack growth velocities. A proposal for amelioration of the problem is offered.