Inserted: 30 mar 2021
Last Updated: 5 jan 2022
Journal: Annales de l'Institut Henri Poincaré / Analyse Nonlinéaire
We investigate variational problems in large-strain magnetoelasticity, both in the static and in the quasistatic setting. The model contemplates a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference configuration, magnetizations are defined on the deformed set in the actual space. In the static setting, we establish the existence of minimizers. In particular, we provide a compactness result for sequences of admissible states with equi-bounded energies which gives the convergence of the composition of magnetizations with deformations. In the quasistatic setting, we consider a notion of dissipation which is frame-indifferent and we show that the incremental minimization problem is solvable. Then, we propose a regularization of the model in the spirit of gradient polyconvexity and we prove the existence of energetic solutions for the regularized model.
Keywords: quasistatic evolutions, magnetoelasticity, large-strain theories, Eulerian-Lagrangian energies