Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 2465 - 2495, Volume 35, Issue 6, June 2015      doi:10.3934/dcds.2015.35.2465

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Michela Eleuteri - Dipartimento di Matematica ed Informatica “U. Dini”, viale Morgagni 67/a, I-50134 Firenze, Italy (email)
Jana Kopfová - Mathematical Institute of the Silesian University, Na Rybníčku 1, 746 01 Opava, Czech Republic (email)
Pavel Krejčí - Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1, Czech Republic (email)

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:  Elastoplastic beam, Prandtl-Ishlinskii operator, material fatigue, thermo-elasto-plasticity, phase transition.
Mathematics Subject Classification:  47J40, 74R20, 74K10, 74N30, 82B26.

Received: December 2013;      Revised: April 2014;      Available Online: December 2014.