Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity
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 , which in turn was inspired by the investigations in  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.
KeywordsPlastic Strain Yield Function Dissipation Function Flow Relation Plastic Range
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.
- 1.Carstensen, C., Ebobisse, F., McBride, A.T., Reddy, B.D., Steinmann, P.: Some properties of the dissipative model of strain-gradient plasticity. Phil. Mag., in press (2017)Google Scholar
- 10.Han, W., Reddy, B.D.: Plasticity: Mathematical Theory and Numerical Analysis. Second Edition, Springer, New York (2013)Google Scholar
- 11.Reddy, B.D.: The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity. Contin. Mech. Thermodyn. 23, 527–549 (2011)Google Scholar