A new asymptotic approach for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations on a single slip plane under the action of an external loading in the direction of a locked dislocation in that plane is considered. As n -> infinity the continuum number density of the dislocations can be easily obtained whereas direct evaluation of the discrete dislocation positions from the set of force balance equations is not straightforward. However, in the framework of our method these positions can be revealed using the corresponding dislocation density.
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