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arXiv · 2511.21907

Homogenization and linearization in magnetoelasticity under small elastic response

Mikhail Cherdantsev·Elisa Davoli·Lorenza D'Elia·Samuele Riccò
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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.

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Mikhail Cherdantsev, Elisa Davoli, Lorenza D'Elia, Samuele Riccò. 2025-11-26. Homogenization and linearization in magnetoelasticity under small elastic response. https://arxiv.org/abs/2511.21907

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