Seminario

"Existence results in magnetoelasticity"

Seminario periodico del Dipartimento di Matematica
1 marzo 2022
Orario di inizio 
13:30
Online
Destinatari: 
Comunità universitaria
Comunità studentesca UniTrento
Partecipazione: 
Online
Referente: 
Prof. Andrea Pinamonti, dott. Andrea Marchese, dott. Giorgio Saracco
Contatti: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
Speaker: 
Marco Bresciani (TU Wien & Uni Wien)

Abstract

We study a variational model of magnetoelasticity both in the static and in the quasistatic setting. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed configuration in the actual space. The magnetic saturation constraint is formulated in the reference configuration and involves the Jacobian determinant of deformations. These belong to the class of possibility discontinuous deformations excluding cavitation introduced by Barchiesi, Henao and Mora-Corral. We establish a compactness result which, in particular, yields the convergence of the compositions of magnetizations with deformations. In the static setting, this result provides the existence of minimizers by means of classical lower semicontinuity methods. Our compactness result also allows us to address the analysis in the quasistatic setting, where we examine rate-independent evolutions driven by applied loads and boundary conditions in presence of dissipative effects. In this case, we achieve the existence of energetic solutions.

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