Continuum dislocation dynamics based on the second order alignment tensor

Thomas Hochrainer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

Original languageEnglish
Article numbermrsf13-1651-kk06-02
JournalMaterials Research Society Symposium Proceedings
Publication statusPublished - 2014


  • dislocations
  • metal
  • microstructure

ASJC Scopus subject areas

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


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