Dislocation Dynamics in Crystals: A Macroscopic Theory in a Fractional Laplace Setting

Serena Dipierro, Giampiero Palatucci, Enrico Valdinoci

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

We consider an evolution equation arising in the Peierls–Nabarro model for crystal dislocation. We study the evolution of such a dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.

Original languageEnglish
Pages (from-to)1061-1105
Number of pages45
JournalCommunications in Mathematical Physics
Volume333
Issue number2
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

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