Scaling of dislocation-based strain-gradient plasticity

Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations


By taking into account the dislocations that are geometrically necessary for producing a curvature or twist of the atomic lattice in crystals, Gao et al. recently developed a theory of strain-gradient plasticity on the micrometer scale and showed that it agrees relatively well with the tests of hardness, torsion and bending of copper on the micrometer scale. This paper subjects this theory to an asymptotic scaling analysis. It is shown that the small-size asymptotic limit of this theory exhibits (1) an unusually strong size effect in which the corresponding nominal stresses in geometrically similar structures of different sizes D vary as D-5/2, and (2) an asymptotic approach to a load-deflection diagram whose tangent stiffness gradually increases, starting with an infinitely small initial stiffness at infinitely small stress. Although this peculiar small-size asymptotic behavior might not be attainable within the practical applicability range of a continuum theory, it renders questionable any efforts to construct approximations of an asymptotic matching character, with a two-sided asymptotic support, which have previously been proven effective for quasibrittle materials such as concrete, rock, ice and fiber composites. A possible simple modification of the existing theory with respect to the small-size asymptotic properties is suggested. However, the questions of experimental justification of such a modification and its compatibility with the dislocation theory will require further study. The small-size asymptotic properties of other strain gradient theories of plasticity have not been analyzed, except for those of the previous Fleck-Hutchinson theory, which have been found reasonable.

Original languageEnglish (US)
Pages (from-to)435-448
Number of pages14
JournalJournal of the Mechanics and Physics of Solids
Issue number3
StatePublished - Mar 2002


  • Asymptotic methods
  • Dislocations
  • Metal plasticity
  • Micromechanics
  • Scaling
  • Size effect
  • Strain gradient

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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