Arrested cracks in nonlinear lattice models of brittle fracture.
We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.
Kessler
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Department of Mathematics, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
Levine
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