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A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector

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Abstract

In this paper, we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor \({{\,\mathrm{Curl}\,}}p\) giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge invariance conditions, i.e., only true state variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn’s inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain \(\mathbf \varepsilon _p\) and standard isotropic hardening.

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Acknowledgements

The research of Francois Ebobisse has been supported by the National Research Foundation (NRF) of South Africa through the Incentive Grant for Rated Researchers and the International Centre for Theoretical Physics (ICTP) through the Associateship Scheme. The first draft of this work was written at Essen (Germany) while Francois Ebobisse was visiting the Faculty of Mathematics of the University of Duisburg-Essen.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, South Africa

    François Ebobisse

  2. Lehrstuhl für Mechanik-Materialtheorie, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801, Bochum, Germany

    Klaus Hackl

  3. Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Str. 9, 45127, Essen, Germany

    Patrizio Neff

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  1. François Ebobisse
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  2. Klaus Hackl
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  3. Patrizio Neff
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Correspondence to François Ebobisse.

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Communicated by Andreas Öchsner.

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Ebobisse, F., Hackl, K. & Neff, P. A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector. Continuum Mech. Thermodyn. 31, 1477–1502 (2019). https://doi.org/10.1007/s00161-019-00755-5

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