Abstract
We study mathematical properties of the model that has been proposed to explain the phenomenon of hardening due to cyclic loading. The model considers two elastic plastic materials, soft and hard, that co-exist while the soft material can be transformed into the hard material. Regarding elastic responses we remain in a simplified framework of linearized elasticity. Incorporating tools such as variational inequalities, penalty approximations and Sobolev spaces, we prove the existence of weak solution to the corresponding boundary-value problem and investigate its uniqueness and regularity.
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Notes
- 1.
Here for simplicity (in order to avoid the compatibility condition on the data), we assume that Γ ≠ ∅.
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Acknowledgements
Jens Frehse work was supported by SFB611 at University of Bonn, Josef Málek work was supported by the project GAČR 107/12/0121.
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Frehse, J., Málek, J. (2014). On Prandtl-Reuss Mixtures. In: Griebel, M. (eds) Singular Phenomena and Scaling in Mathematical Models. Springer, Cham. https://doi.org/10.1007/978-3-319-00786-1_7
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DOI: https://doi.org/10.1007/978-3-319-00786-1_7
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