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Elastoplasticity of gradient-polyconvex materials

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Abstract

We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we prove the existence of the so-called energetic solution. The stored energy density function is assumed to depend on gradients of minors of the deformation gradient which makes our results applicable to shape-memory materials, for instance.

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Acknowledgements

This work was supported by the GAČR projects 18-03834S (MK & JZ), 21-06569K (MK), and by the DFG Priority Programme (SPP) 2256 (JZ).

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Authors and Affiliations

  1. Czech Academy of Sciences, Institute of Information Theory and Automation, Pod vodárenskou veží 4, 182 08, Prague, Czechia

    Martin Kružík

  2. Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29, Prague, Czechia

    Martin Kružík

  3. Institut für Mathematik, Universität Augsburg, D-86135, Augsburg, Germany

    Jiří Zeman

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  1. Martin Kružík
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Correspondence to Martin Kružík.

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Kružík, M., Zeman, J. Elastoplasticity of gradient-polyconvex materials. Z. Angew. Math. Phys. 72, 174 (2021). https://doi.org/10.1007/s00033-021-01603-w

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