Fatigue and phase transition in an oscillating elastoplastic beam

Michela Eleuteri¹ ; Chiara Gavioli¹ ; Jana Kopfová²

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.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 41.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2019052

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