Multipole expansion of continuum dislocation dynamics in terms of alignment tensors

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The development of a dislocation-based continuum theory of plasticity remains one of the central challenges of applied physics and materials science. Developing a continuum theory of dislocations requires the solution of two long-standing problems: (i) to find a faithful representation of dislocation kinematics with a reasonable number of variables and (ii) to derive averaged descriptions of the dislocation dynamics (i.e. material laws) in terms of these variables. In the current paper, we solve the first problem, i.e. we develop tensorial conservation laws for distributions of oriented lines. This is achieved through a multipole expansion of the dislocation density in terms of so-called alignment tensors containing information on the directional distribution of dislocation density and dislocation curvature. A hierarchy of evolution equations of these tensors is derived from a higher dimensional dislocation density theory. Low-order closure approximations of this hierarchy lead to continuum dislocation dynamics models of plasticity with only few internal variables. Perspectives for more refined theories and current challenges in dislocation density modelling are discussed. © 2015 © 2015 Taylor & Francis.
Original languageEnglish
Pages (from-to)1321-1367
JournalPhilosophical Magazine / Letters
Publication statusPublished - 2015


  • alignment tensors
  • crystal plasticity
  • dislocations
  • multipole expansion

ASJC Scopus subject areas

  • Mechanics of Materials

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