# American Institute of Mathematical Sciences

November  2013, 12(6): 2973-2996. doi: 10.3934/cpaa.2013.12.2973

## Non-isothermal cyclic fatigue in an oscillating elastoplastic beam

 1 Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133 Milano. 2 Mathematical Institute of the Silesian University, Na Rybníčku 1, 746 01 Opava 3 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1

Received  July 2012 Revised  February 2013 Published  May 2013

We propose a temperature dependent model for fatigue accumulation in an oscillating elastoplastic beam. The full system consists of the momentum and energy balance equations, and an evolution equation for the fatigue rate. The main modeling hypothesis is that the fatigue accumulation rate is proportional to the dissipation rate. In nontrivial cases, the process develops a thermal singularity in finite time. The main result consists in proving the existence and uniqueness of a strong solution in a time interval depending on the size of the data.
Citation: Michela Eleuteri, Jana Kopfová, Pavel Krejčí. Non-isothermal cyclic fatigue in an oscillating elastoplastic beam. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2973-2996. doi: 10.3934/cpaa.2013.12.2973
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