Magnetoelastic thin films at large strains

Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of $$\varGamma $$ Γ -convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model features both Lagrangian and Eulerian terms. This calls for qualifying admissible three-dimensional deformations of planar domains in terms of injectivity. In addition, a careful treatment of the Maxwell system in the deformed film is required.