Numerical implementation of continuum dislocation dynamics with the discontinuous-Galerkin method

Alireza Ebrahimi*, Mehran Monavari, Thomas Hochrainer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

Original languageEnglish
Article number605
JournalMaterials Research Society Symposium Proceedings
Publication statusPublished - 2014


  • crystalline
  • dislocations
  • microstructure

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanical Engineering
  • Mechanics of Materials


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