Existence results for incompressible magnetoelasticity

We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference configuration, magnetization is defined in the deformed configuration instead. We discuss the existence of energy minimizers without relying on higher-order deformation gradient terms. Then, by introducing a suitable positively $1$-homogeneous dissipation, a quasistatic evolution model is proposed and analyzed within the frame of energetic solvability.