Homogenization and linearization in magnetoelasticity under small elastic response
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908677659688960 |
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| author | Cherdantsev, Mikhail Davoli, Elisa D'Elia, Lorenza Riccò, Samuele |
| author_facet | Cherdantsev, Mikhail Davoli, Elisa D'Elia, Lorenza Riccò, Samuele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homogenization and linearization in magnetoelasticity under small elastic response Cherdantsev, Mikhail Davoli, Elisa D'Elia, Lorenza Riccò, Samuele Analysis of PDEs 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. |
| title | Homogenization and linearization in magnetoelasticity under small elastic response |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.21907 |