Cohesive zone models provide an illuminating and tractable way to include constitutive non-linearity into continuum models of defects. Powerful insights have been gained by studying both dislocations and cracks using such analyses. Recent work has shown that as a result of the locality assumption present in such cohesive zone models, significant errors can be made in the treatment of defect energies. This paper aims to construct a non-local version of the Peierls-Nabarro model in which the atomic level stresses induced at the slip plane depend in a non-local way on the slip degrees of freedom. Our results should be seen as a demonstration in principle of how microscopic calculations can be used to construct insights into constitutive nonlocality. The non-local interplanar kernel used here is computed directly from atomistics and is used to evaluate both the structure and energetics of planar dislocations. The non-local formulation does not significantly change the dislocation core structure from that obtained with the local model, but the new formulation leads to significant improvements in the description of dislocation energetics for dislocations with planar cores.

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Journal Journal of the Mechanics and Physics of Solids
Miller, R. E, Phillips, R. (Rob), Beltz, G. (Glen), & Ortiz, M. (Michael). (1998). A non-local formulation of the Peierls dislocation model. Journal of the Mechanics and Physics of Solids, 46(10), 1845–1867.