English

Homogenization and linearization in magnetoelasticity under small elastic response

Analysis of PDEs 2025-12-01 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2511.21907,
  title  = {Homogenization and linearization in magnetoelasticity under small elastic response},
  author = {Mikhail Cherdantsev and Elisa Davoli and Lorenza D'Elia and Samuele Riccò},
  journal= {arXiv preprint arXiv:2511.21907},
  year   = {2025}
}
R2 v1 2026-07-01T07:57:08.796Z