On the formulations of higher-order strain gradient crystal plasticity models

M. Kuroda, Viggo Tvergaard

    Research output: Contribution to journalJournal articleResearchpeer-review


    Recently, several higher-order extensions to the crystal plasticity theory have been proposed to incorporate effects of material length scales that were missing links in the conventional continuum mechanics. The extended theories are classified into work-conjugate and non-work-conjugate types. A common feature of the former is that existence of higher-order stresses work-conjugate to gradients of plastic strain is presumed and an extended principle of virtual work involving such an additional virtual work contribution is formulated. Meanwhile, in the latter type, the higher-order stress quantities do not appear explicitly. Instead, rates of crystallographic slip are influenced by back stresses that arise in response to spatial gradients of the geometrically necessary dislocation densities. The work-conjugate type and the non-work-conjugate type of theories have different theoretical backgrounds and very unlike mathematical representations. Nevertheless, both types of theories predict the same kind of material length scale effects. We have recently shown that there exists some equivalency between the two approaches in the special situation of two-dimensional single slip under small deformation. In this paper, the discussion is extended to a more general situation, i.e. the context of multiple and three-dimensional slip deformations.
    Original languageEnglish
    JournalJournal of the Mechanics and Physics of Solids
    Issue number4
    Pages (from-to)1591-1608
    Publication statusPublished - 2008


    • metals
    • dislocations
    • constitutive behavior
    • material length scales
    • finite elements


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