A finite deformation theory of higher-order gradient crystal plasticity

Mitsutoshi Kuroda, Viggo Tvergaard

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    For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation (GND) densities supplement the conventional theory within a non-work-conjugate framework in which there is no need to introduce higher-order microscopic stresses that would be work-conjugate to slip rate gradients. We discuss its connection to a work-conjugate type of finite deformation gradient crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution for the small deformation theory. As in a previous formulation for small deformation, the present formulation applies to the context of multiple and three-dimensional slip deformations. (C) 2008 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    JournalJournal of the Mechanics and Physics of Solids
    Issue number8
    Pages (from-to)2573-2584
    Publication statusPublished - 2008


    • constitutive behavior
    • crystal plasticity
    • dislocations
    • material length scales
    • finite deformations


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