Effective theories for incompressible magnetoelastic shallow shells
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915451612692480 |
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| author | Tasso, Emanuele Unterberger, Tobias |
| author_facet | Tasso, Emanuele Unterberger, Tobias |
| contents | We characterize the asymptotic behaviour, in the sense of $Γ$-convergence, of a thin magnetoelastic shallow shell. The compactness is achieved up to rigid motions. For deformations, it relies on an approximation by rigid movements, whereas for magnetizations it is based on a careful consideration of the geometry of the deformed domain. The result is obtained by a combination of variational methods ($Γ$-convergence) with degree theory, fixed-point and geometrical arguments. The proof strategy relies on an adaptation of an analogous result for incompressible magnetoelastic plates from M. Bresciani in arXiv:2007.14122 and an application of results by I.Velcic on elastic shallow shells in arXiv:1102.2647. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective theories for incompressible magnetoelastic shallow shells Tasso, Emanuele Unterberger, Tobias Analysis of PDEs We characterize the asymptotic behaviour, in the sense of $Γ$-convergence, of a thin magnetoelastic shallow shell. The compactness is achieved up to rigid motions. For deformations, it relies on an approximation by rigid movements, whereas for magnetizations it is based on a careful consideration of the geometry of the deformed domain. The result is obtained by a combination of variational methods ($Γ$-convergence) with degree theory, fixed-point and geometrical arguments. The proof strategy relies on an adaptation of an analogous result for incompressible magnetoelastic plates from M. Bresciani in arXiv:2007.14122 and an application of results by I.Velcic on elastic shallow shells in arXiv:1102.2647. |
| title | Effective theories for incompressible magnetoelastic shallow shells |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.13916 |