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

Alireza Ebrahimi, Mehran Monavari, Thomas Hochrainer

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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
JournalMaterials Research Society Symposium Proceedings
Volume1651
DOIs
Publication statusPublished - 2014

Fingerprint

Galerkin method
Galerkin methods
Dislocations (crystals)
Plasticity
continuums
Crystals
plastic properties
Fluxes
curvature
crystals
slip

Keywords

  • crystalline
  • dislocations
  • microstructure

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Numerical implementation of continuum dislocation dynamics with the discontinuous-Galerkin method. / Ebrahimi, Alireza; Monavari, Mehran; Hochrainer, Thomas.

In: Materials Research Society Symposium Proceedings, Vol. 1651, 2014.

Research output: Contribution to journalArticleResearchpeer-review

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