Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

Alireza Ebrahimi, Thomas Hochrainer

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


A persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.

In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus® in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.
Original languageEnglish
Title of host publicationMRS Advances
Publication statusPublished - 2016
Externally publishedYes


  • dislocations
  • defects
  • microstructure

ASJC Scopus subject areas

  • Materials Science(all)


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