A phase field crystal theory of the kinematics of dislocation lines

Research output: Contribution to journalResearch articleContributedpeer-review


  • Vidar Skogvoll - , University of Oslo (Author)
  • Luiza Angheluta - , University of Oslo (Author)
  • Audun Skaugen - , University of Oslo (Author)
  • Marco Salvalaglio - , Institute of Scientific Computing (Author)
  • Jorge Viñals - , University of Minnesota System (Author)


We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach–Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.


Original languageEnglish
Article number104932
Number of pages19
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - Sept 2022

External IDs

WOS 000814571000004
ORCID /0000-0002-4217-0951/work/142237447


DFG Classification of Subject Areas according to Review Boards


  • Atomistic models, Computational methods, Crystal plasticity, Dislocation dynamics, Phase-field crystal modeling, Structure of solids and liquids, DYNAMICS, SIMULATIONS, MICROSTRUCTURE

Library keywords