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.
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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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Carstensen, C., Ebobisse, F., McBride, A.T., Reddy, B.D., Steinmann, P. (2017). Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity. In: dell'Isola, F., Sofonea, M., Steigmann, D. (eds) Mathematical Modelling in Solid Mechanics. Advanced Structured Materials, vol 69. Springer, Singapore. https://doi.org/10.1007/978-981-10-3764-1_3
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DOI: https://doi.org/10.1007/978-981-10-3764-1_3
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