Cherdantsev, M., Davoli, E., D’Elia, L., & Ricco, S. (2025). Homogenization and linearization in magnetoelasticity under small elastic response. https://doi.org/10.48550/arXiv.2511.21907
We perform a simultaneous homogenization and linearization analysis for a magnetoelastic energy functional featuring a mixed Eulerian-Lagrangian structure. Neglecting Zeeman and anisotropic contributions, we characterize the asymptotic behavior in the sense of Gamma-convergence for the sum of a nonlinear magnetoelastic energy, a symmetric exchange term defined on the actual configuration, and for the associated magnetostatic self-energy. After establishing compactness of displacements and magnetizations with equibounded energy, we identify the limiting energy functional as the sum of a quadratic homogenized magnetoelastic contribution with a limiting homogenized exchange and magnetostatic term. This is, to the authors' knowledge, the first homogenization result for manifold-valued mixed Eulerian-Lagrangian energies.
