| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|
|
|---|---|---|
| Article Number | 41 | |
| Number of page(s) | 27 | |
| DOI | https://doi.org/10.1051/mmnp/2019052 | |
| Published online | 22 September 2020 | |
Fatigue and phase transition in an oscillating elastoplastic beam*
1
University of Modena and Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche,
via Campi 213/b,
41125
Modena, Italy.
2
Mathematical Institute of the Silesian University,
Na Rybníčku 1,
746 01
Opava, Czech Republic.
** Corresponding author: michela.eleuteri@unimore.it
Received:
27
December
2018
Accepted:
17
November
2019
We study a model of fatigue accumulation in an oscillating elastoplastic beam under the hypothesis that the material can partially recover by the effect of melting. The model is based on the idea that the fatigue accumulation is proportional to the dissipated energy. We prove that the system consisting of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics admits a unique strong solution.
Mathematics Subject Classification: 47J40 / 74R20 / 74K10 / 74N30 / 82B26
Supported by the institutional support for the development of research organizations IČ 47813059. The work of the first two authors is supported by GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica), by the University of Modena and Reggio Emilia through the project FAR2017 “Equazioni differenziali: problemi evolutivi, variazionali ed applicazioni” (coord. Prof. S. Gatti) and by MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca) through the project FFABR2017.
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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