Numerical implementation of static Field Dislocation Mechanics theory for periodic media

R. Brenner, A. J. Beaudoin, P. Suquet, A. Acharya

Research output: Contribution to journalArticlepeer-review


This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.

Original languageEnglish (US)
Pages (from-to)1764-1787
Number of pages24
JournalPhilosophical Magazine
Issue number16
StatePublished - Jun 3 2014


  • Field Dislocation Mechanics
  • Fourier transform
  • infinite bicrystal
  • internal stresses
  • periodic microstructure
  • zero-stress dislocation distributions

ASJC Scopus subject areas

  • Condensed Matter Physics


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