On the Structure of Linear Dislocation Field Theory

Amit Acharya, Robin Knops, Jeyabal Sivaloganathan

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Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is illustrated by a specific example that clarifies the use of the plasticity formulation in the study of classical dislocation theory. Stationary, quasi-static, and dynamical problems for continuous dislocation distributions are investigated subject not only to standard boundary and initial conditions, but also to prescribed dislocation density. In particular, the dislocation density field can represent a single dislocation line.

It is only in the static and quasi-static traction boundary value problems that such data are sufficient for the unique determination of stress. In other quasi-static boundary value problems and problems involving moving dislocations, the plastic and elastic distortion tensors, total displacement, and stress are in general non-unique for specified dislocation density. The conclusions are confirmed by the example of a single screw dislocation.

Original languageEnglish
Pages (from-to)216-244
Number of pages29
JournalJournal of the Mechanics and Physics of Solids
Early online date8 Jun 2019
Publication statusPublished - 1 Sept 2019


  • Dislocations
  • Elasticity
  • Plasticity
  • Uniqueness
  • Volterra

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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