Moving dislocations in finite plasticity: a topological approach

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Here the author derives the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Original languageEnglish
Pages (from-to)252-268
JournalZeitschrift für angewandte Mathematik und Mechanik
Volume93
Issue number4
DOIs
Publication statusPublished - 2013

Fingerprint

Dislocation
Plasticity
Dislocations (crystals)
Crystals
Tensors
Plastic deformation
Kinematics
Evolution Equation
Crystal
Continuum
Finite Deformation
Motion
Kink
Plastic Deformation
Large Deformation
Tensor
Formulation
Modeling

Keywords

  • Differential topology
  • Dislocations
  • Finite plasticity

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Moving dislocations in finite plasticity: a topological approach. / Hochrainer, Thomas.

In: Zeitschrift für angewandte Mathematik und Mechanik, Vol. 93, No. 4, 2013, p. 252-268.

Research output: Contribution to journalArticleResearchpeer-review

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