Existence results in large-strain magnetoelasticity

Marco Bresciani (TU Wien & Uni Wien)

Abstract:

We investigate problems in magnetoelasticity, including the Dzyaloshinskii-Moriya interaction. In the large-strain regime, the model features a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference configuration (Lagrangian), magnetizations are defined on the deformed set (Eulerian), which is a priori unknown. This setting leads to various mathematical difficulties that require an in-depth study of fine and invertibility properties of admissible deformations to be overcome. First, we discuss the existence of minimizers of the energy in the static case; then, we address the existence of energetic solutions driven by the energy and a rate-independent dissipation. This is joint work with Elisa Davoli (TU Wien) and Martin Kruzík (Czech Academy of Science).