Journal of Nonlinear Science

, Volume 29, Issue 1, pp 319–344 | Cite as

Variational Evolution of Dislocations in Single Crystals

  • Riccardo Scala
  • Nicolas Van GoethemEmail author


In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem consists of a polyconvex stored elastic energy plus a dislocation energy and some higher-order terms. The dislocations are modeled by means of integral one-currents. Moreover, we discuss a novel dissipation structure for such currents, namely the flat distance, that will serve to drive the evolution of the dislocation clusters.


Dislocation clusters Finite elasticity Time evolution Energetic solutions Variational method 

Mathematics Subject Classification

35Q74 74B20 35A15 74G65 49Q15 



We acknowledge the support of the FCT Starting Grant “ Mathematical theory of dislocations: geometry, analysis, and modeling” (IF/00734/2013). We thank the anonymous referees for their careful reading and interesting suggestions, which allow us to deeply improve our discussion.


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Authors and Affiliations

  1. 1.Universidade de Lisboa, Faculdade de Ciências, CMAF_CIOAlameda da UniversidadeLisboaPortugal

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