A mathematical basis for strain-gradient plasticity theory—Part I: Scalar plastic multiplier |
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Authors: | NA Fleck JR Willis |
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Institution: | a Cambridge University Engineering Department, Trumpington St., Cambridge CB2 1PZ, UK b Department of Applied Mathematics and Theoretical Physics, Wilberforce Rd, Cambridge CB3 0WA, UK |
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Abstract: | Strain-gradient plasticity theories are reviewed in which some measure of the plastic strain rate is treated as an independent kinematic variable. Dislocation arguments are invoked in order to provide a physical basis for the hardening at interfaces. A phenomenological, flow theory version of gradient plasticity is constructed in which stress measures, work-conjugate to plastic strain and its gradient, satisfy a yield condition. Plastic work is also done at internal interfaces and a yield surface is postulated for the work-conjugate stress quantities at the interface. Thereby, the theory has the potential to account for grain size effects in polycrystals. Both the bulk and interfacial stresses are taken to be dissipative in nature and due attention is paid to ensure that positive plastic work is done. It is shown that the mathematical structure of the elasto-plastic strain-gradient theory has similarities to conventional rigid-plasticity theory. Uniqueness and extremum principles are constructed for the solution of boundary value problems. |
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Keywords: | Strain-gradient plasticity Size effects Variational principle Interface effects |
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