A three-dimensional continuum theory of dislocation systems: Kinematics and mean-field formulation

T. Hochrainer*, M. Zaiser, P. Gumbsch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose a dislocation density measure which is able to account for the evolution of systems of three-dimensional curved dislocations. The definition and evolution equation of this measure arise as direct generalizations of the definition and kinematic evolution equation of the classical dislocation density tensor. The evolution of this measure allows us to determine the plastic distortion rate in a natural fashion and therefore yields a kinematically closed dislocation-based theory of plasticity. A self-consistent theory is built upon the measure which accounts for both the long-range interactions of dislocations and their short-range self-interaction which is incorporated via a line-tension approximation. A two-dimensional kinematic example illustrates the definitions and their relations to the classical theory.

Original languageEnglish
Pages (from-to)1261-1282
Number of pages22
JournalThe Philosophical Magazine
Issue number8-9
Publication statusPublished - Mar 2007

ASJC Scopus subject areas

  • Mechanical Engineering

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