A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals

Kazuyuki Shizawa, H. M. Zbib

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A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. Thermodynamically consistent constitutive equations for plastic stretching, plastic spin and back stress are rigorously derived. Also, an expression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present gradient theory yields a symmetric stress tensor. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given.

Original languageEnglish
Pages (from-to)899-938
Number of pages40
JournalInternational Journal of Plasticity
Issue number9
Publication statusPublished - 1999



  • Constitutive behavior
  • Dislocation density tensor
  • Elastic-plastic material
  • Finite strain
  • Thermomechanical processes

ASJC Scopus subject areas

  • Mechanical Engineering

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