Preprint
Balanced Viscosity solutions to a rate-independent system for damage
Zusammenfassung
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the displacement and damage fields. Thus, we are in a position to work with a stronger solution notion at the level of the viscous approximating system. The vanishing-viscosity analysis then leads us to obtain the existence of a stronger solution concept for the rate-independent limit system. Furthermore, in comparison to [KRZ13, KRZ15], in our vanishing-viscosity analysis we do not switch to an artificial arc-length parameterization of the trajectories but we stay with the true physical time. The resulting concept of Balanced Viscosity solution to the rate-independent damage system thus encodes a more explicit characterization of the system behavior at time discontinuities of the solution.
Förderhinweis
DFG-Priority Program SPP 1962, GNAMPA (INDAM)Zitieren
@article{urn:nbn:de:hebis:34-2017050252462,
author={Knees, Dorothee and Rossi, Riccarda and Zanini, Chiara},
title={Balanced Viscosity solutions to a rate-independent system for damage},
year={2017}
}
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2017-05-02T07:10:24Z 2017-05-02T07:10:24Z 2017-05-02 urn:nbn:de:hebis:34-2017050252462 http://hdl.handle.net/123456789/2017050252462 DFG-Priority Program SPP 1962, GNAMPA (INDAM) eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ balanced viscosity rate-independent system damage model 510 Balanced Viscosity solutions to a rate-independent system for damage Preprint This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the displacement and damage fields. Thus, we are in a position to work with a stronger solution notion at the level of the viscous approximating system. The vanishing-viscosity analysis then leads us to obtain the existence of a stronger solution concept for the rate-independent limit system. Furthermore, in comparison to [KRZ13, KRZ15], in our vanishing-viscosity analysis we do not switch to an artificial arc-length parameterization of the trajectories but we stay with the true physical time. The resulting concept of Balanced Viscosity solution to the rate-independent damage system thus encodes a more explicit characterization of the system behavior at time discontinuities of the solution. open access Knees, Dorothee Rossi, Riccarda Zanini, Chiara Mathematische Schriften Kassel ;; 17, 02 Mathematische Schriften Kassel 17, 02
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