An alternative treatment of phenomenological higher-order strain-gradient plasticity theory

Mitsutoshi Kuroda, Viggo Tvergaard

Research output: Contribution to journalJournal articleResearchpeer-review


Phenomenological higher-order strain-gradient plasticity is here presented through a formulation inspired by previous work for strain-gradient crystal plasticity. A physical interpretation of the phenomenological yield condition that involves an effect of second gradient of the equivalent plastic strain is discussed, applying a dislocation theory-based consideration. Then, a differential equation for the equivalent plastic strain-gradient is introduced as an additional governing equation. Its weak form makes it possible to deduce and impose extra boundary conditions for the equivalent plastic strain. A connection between the present treatment and strain-gradient theories based on an extended virtual work principle is discussed. Furthermore, a numerical implementation and analysis of constrained simple shear of a thin strip are presented.
Original languageEnglish
JournalInternational Journal of Plasticity
Issue number4
Pages (from-to)507-515
Publication statusPublished - 2010


  • Constitutive behavior
  • Dislocations
  • Strain-gradient plasticity
  • Size effects


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