It was noted that cohesive-zone models provided a revealing and tractable method for incorporating constitutive non-linearity into continuum models of defects. Useful insights were obtained by studying dislocations using such analyses. It had been shown that, as a result of the locality assumption which was implicit in such cohesive-zone models, significant errors could be made in the treatment of defect energies. A non-local version of the Peierls-Nabarro model was constructed here, in which the atomic-level stresses which were induced at the slip-plane depended in a non-local way upon the slip degrees of freedom. The results were considered to be a demonstration of how microscopic calculations could be used to achieve insights into constitutive non-locality. The non-local interplanar kernel which was used here was calculated directly from atomistics and was used to evaluate the structure and energetics of planar dislocations. The non-local formulation did not significantly change the dislocation core structure from that which was obtained by using the local model, but the new formulation led to significant improvements in the description of dislocation energetics for dislocations with planar cores.

A Non-Local Formulation of the Peierls Dislocation Model. R.Miller, R.Phillips, G.Beltz, M.Ortiz: Journal of the Mechanics and Physics of Solids, 1998, 46[10], 1845-67