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arXiv · 2508.13916

Effective theories for incompressible magnetoelastic shallow shells

Emanuele Tasso·Tobias Unterberger
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Abstract

We characterize the asymptotic behaviour, in the sense of $\Gamma$-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 ($\Gamma$-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.

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Emanuele Tasso, Tobias Unterberger. 2025-08-19. Effective theories for incompressible magnetoelastic shallow shells. https://arxiv.org/abs/2508.13916

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