Variational Evolution of Dislocations in Single Crystals

@article{Scala2019VariationalEO,
  title={Variational Evolution of Dislocations in Single Crystals},
  author={Riccardo Scala and Nicolas Van Goethem},
  journal={Journal of Nonlinear Science},
  year={2019},
  volume={29},
  pages={319-344}
}
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. 
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