We study the effect of general nonlinear force laws in viscoelastic lattice models of fracture, focusing on the existence and stability of steady-state mode III cracks. We show that the hysteretic behavior at small driving is very sensitive to the smoothness of the force law. At large driving, we find a Hopf bifurcation to a straight crack whose velocity is periodic in time. The frequency of the unstable bifurcating mode depends on the smoothness of the potential, but is very close to an exact period-doubling instability. Slightly above the onset of the instability, the system settles into a exactly period-doubled state, presumably connected to the aforementioned bifurcation structure. We explicitly solve for this new state and map out its velocity-driving relation.

• Received 10 July 2000

DOI:https://doi.org/10.1103/PhysRevE.63.016118