Existence results in large-strain magnetoelasticity

  • Marco Bresciani

    TU Wien, Austria
  • Elisa Davoli

    TU Wien, Austria
  • Martin Kružík

    Czech Academy of Sciences, Prague, Czech Republic; Czech Technical University, Prague, Czechia
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We investigate variational problems in large-strain magnetoelasticity, in both the static and the quasistatic settings. 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.

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Marco Bresciani, Elisa Davoli, Martin Kružík, Existence results in large-strain magnetoelasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 3, pp. 557–592

DOI 10.4171/AIHPC/51