A new phase field model for material fatigue in an oscillating elastoplastic beam

Michela Eleuteri; Jana Kopfová; Pavel Krejčí

doi:10.3934/dcds.2015.35.2465

Article Contents

2015, Volume 35, Issue 6: 2465-2495. Doi: 10.3934/dcds.2015.35.2465

This issue Previous Article Some mathematical problems related to the second order optimal shape of a crystallisation interface Next Article On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids

A new phase field model for material fatigue in an oscillating elastoplastic beam

1.
Dipartimento di Matematica ed Informatica “U. Dini”, viale Morgagni 67/a, I-50134 Firenze
2.
Mathematical Institute of the Silesian University, Na Rybníčku 1, 746 01 Opava
3.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1

Received: December 2013

Revised: April 2014

Published: May 2017

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Abstract

We pursue the study of fatigue accumulation in an oscillating elastoplastic beam under the additional hypothesis that the material can partially recover by the effect of melting. The full system consists of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics. The main result consists in proving the existence and uniqueness of a strong solution.

Keywords:

Mathematics Subject Classification: 47J40, 74R20, 74K10, 74N30, 82B26.

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References

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