Calculus of Variations and Geometric Measure Theory
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M. Bresciani - E. Davoli - M. Kruzik

Existence results in large-strain magnetoelasticity with asymmetric exchange energy

created by davoli on 30 Mar 2021

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Submitted Paper

Inserted: 30 mar 2021
Last Updated: 30 mar 2021

Year: 2021

Abstract:

We investigate problems in large-strain magnetoelasticity when a Dzyaloshinskii-Moriya interaction term is included, too. While the magnetoelastic stored energy density is described in the Lagrangean setting, purely magnetic terms are considered in the Eulerian one. This requires careful treatment of the invertibility of admissible elastic deformations and of the regularity of the inverse maps. Besides the existence of a minimizer in the static case, we also show that the model can be extended to an evolutionary situation and enriched by a rate-independent dissipation. In this case, we prove that an energetic solution exists.

Keywords: quasistatic evolution, magnetoelasticity, chirality, Eulerian-Lagrangean energies, large-strain theories


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