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Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity

  • Carsten Carstensen
  • François Ebobisse
  • Andrew T. McBride
  • B. Daya Reddy
  • Paul Steinmann
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 69)

Abstract

In this work we carry out a theoretical investigation of a dissipative model of rate-independent strain-gradient plasticity. The work builds on the investigation in [1], which in turn was inspired by the investigations in [4] of responses to non-proportional loading in the form of surface passivation. We recall the global nature of the flow relation when expressed in terms of the Cauchy stress and dissipation function. We highlight the difficulties encountered in attempts to obtain dual forms of the flow relation and associated yield functions, for the continuous and discrete problems, and derive upper bounds on the global yield function.

Keywords

Plastic Strain Yield Function Dissipation Function Flow Relation Plastic Range 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The work reported in this paper was carried out with support through the South African Research Chair in Computational Mechanics to BDR and ATMcB. This support is gratefully acknowledged. PS acknowledges support through the Collaborative Research Center 814.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Carsten Carstensen
    • 1
  • François Ebobisse
    • 2
  • Andrew T. McBride
    • 3
  • B. Daya Reddy
    • 2
  • Paul Steinmann
    • 4
  1. 1.Humboldt-Universität Zu BerlinBerlinGermany
  2. 2.University of Cape TownCape TownSouth Africa
  3. 3.The University of GlasgowGlasgowUK
  4. 4.University of Erlangen-NurembergErlangenGermany

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