I will present a resent result obtained in collaboration with Elisa Davoli (TU Wien) regarding a high-contrast homogenization problem in magnetoelasticity in the small strain regime. For some heterogeneous material made up by two components exhibiting highly different material properties, we studied a special form of the Gibbs–Landau energy functional of micromagnetics that includes a contribution penalizing the stress related strain in terms of the displacement. We include this term in the fashion of linearized elasticity. By this, the model couples magnetization and deformation of the material and accounts for magnetoelastic (magnetostrictive) effects that arise due to special crystal structures. We also included into the free energy functional the Dzyaloshinskii–Moriya interaction term (DMI) that is known to enable the emergence of magnetic skyrmions. During the homogenization procedure a major challenge consists in taking care of the target manifold confinement dictating that due to the well-known saturation constraint the magnetization should always take values in the sphere. We tackle this by making use of a newly developed extension operator in a work by C. Gavioli, L. Happ, and V. Pagliari (2024), and special approximations for functions with values in the sphere due to F. Bethuel and X. Zheng (1988).

This event takes place in hybrid form (in person and online on Zoom). Slides and additional materials are available on the Moodle service of the University of Vienna. If you want to participate, please write an email to matteo.tommasini@univie.ac.at.