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

Abstract

In this paper, a strain-gradient plasticity model is derived from a mesoscopic model for straight parallel edge dislocations in an infinite cylindrical crystal. The main difference to existing work is that in this work the well-separateness of disloactions is not assumed. In order to prove meaningful lower bounds the ball construction technique, which was developed in the 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 ball construction a combination of combinatorial arguments and local modifications of the occurring elastic strains is presented.

arXiv comment37 pages, 5 figures

References in corpus (1)

• Singular kernels, multiscale decomposition of microstructure, and dislocation models

Cited by in corpus (5)

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• Coarse-graining of a discrete model for edge dislocations in the regular triangular lattice
• A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
• From Volterra dislocations to strain-gradient plasticity