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In this paper, a strain-gradient plasticity model is derived from amesoscopic model for straight parallel edge dislocations in an infinitecylindrical crystal. The main difference to existing work is that in this workthe well-separateness of disloactions is not assumed. In order to provemeaningful lower bounds the ball construction technique, which was developed inthe context of Ginzburg-Landau by Jerrard and Sandier, is adapted and modified.To overcome the difficulty of a loss of rigidity on thin annuli during the ballconstruction a combination of combinatorial arguments and local modificationsof the occurring elastic strains is presented.

Plasticity as the $\Gamma$-Limit of a Two-Dimensional Dislocation Energy: the Critical Regime without the Assumption of Well-Separateness