Asymptotics in discrete dislocation pile-up modelling

An asymptotic methodology for analysing pile-ups of large numbers of dislocations is proposed. We provide robust proof of the interconnection between continuum and discrete approaches to dislocation description. The practical usefulness of the technique is tested on a pile-up of screw or edge dislocations in a uniform material stressed against a lock. The approach is extended to the case of a pile-up of screw dislocations stressed against an interface in a bimetallic solid. The dislocations are located with sufficient accuracy to predict the large but finite stress distribution close the interface. Such a prediction is impossible using a conventional continuum dislocation theory.