Calculus of Variations and Geometric Measure Theory

M. Bresciani

Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions

created by bresciani on 16 Mar 2022
modified on 20 Jul 2023


Published Paper

Inserted: 16 mar 2022
Last Updated: 20 jul 2023

Journal: Calculus of Variations and Partial Differential Equations
Volume: 62
Number: 7
Pages: Article no. 181
Year: 2023


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 enables us to prove 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 this case, we prove the existence of energetic solutions.