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arXiv · 1805.12195

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

Janusz Ginster
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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.

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Janusz Ginster. 2018-05-30. Plasticity as the $Γ$-Limit of a Two-Dimensional Dislocation Energy: the Critical Regime without the Assumption of Well-Separateness. https://doi.org/10.1007/s00205-019-01378-5

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