The mechanics of fracture propagation provides essential knowledge for the risk tolerant design of devices, structures, and vehicles. Ideally fracture should emerge naturally from a field theory described by an initial boundary problem. Nonlocal approaches to fracture modeling are formulated along these lines, coupling fracture caused by breaking bonds at the atomic scale with continuous and discontinuous deformation at the macroscopic scale. Both localization and emergent behavior is the hallmark of theory and simulations using Peridynamic formulations.
In this talk we first discuss the role of nonlocal potentials and multi-scaling as it relates to fracture toughness, kinetic relations, and the flow of elastic energy into singularities. Second we address computational implementations with applications to dynamic and quasi-static fracture and large particle flow simulations (joint work with Debdeep Bhattacharya).
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