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An alternative treatment of phenomenological higher-order strain-gradient plasticity theory
Authors:Mitsutoshi Kuroda  Viggo Tvergaard
Affiliation:1. Graduate School of Science and Engineering, Mechanical Systems Engineering, Yamagata University, Jonan 4-3-16, Yamagata 992-8510, Japan;2. Department of Mechanical Engineering, Solid Mechanics, The Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
Abstract: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.
Keywords:Strain-gradient plasticity   Size effects   Dislocations   Constitutive behavior
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