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Robert Lipton's blog

Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics

Overview: The peridynamic formulation is a
spatially nonlocal derivative free model for simulating problems of free crack
propagation.Material points interact through short-range forces and the
formulation allows for discontinuous deformations. Here the short-range forces
are initially elastic and soften beyond a critical relative displacement. We
upscale this peridynamic model to find the macroscopic (a.k.a. small horizon)
limit. It is shown that the limiting macroscopic evolution has bounded energy
given by the bulk and surface energies of brittle fracture mechanics. The
macroscopic evolution corresponds to the simultaneous evolution
of the fracture surface and linear elastic displacement away from the crack

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