DYNAMIC STABILITY OF ONE-DIMENSIONAL MODELS OF FRACTURE

We examine the linear stability of steady-state propagating fracture i n two one-dimensional models. Both of these models include a cohesive force at the crack tip; they differ only in that the dissipative mecha nism is a frictional force in the first model and a viscosity in the s econd. Our strategy is to compute the Linear response of this system t o a spatially periodic perturbation. As expected, we find no dynamical instabilities in these models. However, we do find some interesting a nalytic properties of the response coefficient that we expect to be re levant to the analysis of more realistic two-dimensional models.