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Origin of crack tip instabilities. (English) Zbl 0878.73053
This paper demonstrates that rapid fracture of ideal brittle lattices naturally involves phenomena long seen in experiment, but which have been hard to understand from a continuum point of view. These idealized models do not mimic realistic microstructure, but can be solved exactly and understood completely. First it is shown that constant velocity crack solutions do not exist at all for a range of velocities starting at zero and ranging up to about one quarter of the shear wave speed. Next it is shown that above this speed cracks are by and large linearly stable, but that at sufficiently high velocity they become unstable with respect to a nonlinear microcracking instability.

MSC:
74R99 Fracture and damage
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