It was noted that the use of continuous distributions of dislocations to model plasticity was usually confined to the analysis of crack-tip plasticity using linear arrays of dislocations within the framework of plane analysis. By extending this technique to treat a distribution of dislocations over an area, a method was developed which could model the plasticity at stress-raising features such as notches or holes under plane-strain conditions. The method explicitly took account of the boundary conditions by using a dislocation solution which accounted for the presence of the stress-raiser itself. Other free boundaries could be modelled more approximately by using boundary elements which also correctly included the presence of the stress raiser. The dislocations were distributed over finite-sized cells, and the solutions which were found for the strain fields compared favourably with finite-element results.

The Distributed Dislocation Method Applied to the Analysis of Elastoplastic Strain Concentrations. P.M.Blomerus, D.A.Hills, P.A.Kelly: Journal of the Mechanics and Physics of Solids, 1999, 47[5], 1007-26