Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911291604467712 |
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| author | Buryachenko, Kateryna Glitzky, Annegret Liero, Matthias Zwicknagl, Barbara |
| author_facet | Buryachenko, Kateryna Glitzky, Annegret Liero, Matthias Zwicknagl, Barbara |
| contents | We study the finite deformation of a thin, elastically heterogeneous sheet subject to electrostatic coupling. The interaction between mechanics and electrostatics is formulated as a saddle-point problem involving the deformation and the electrostatic potential. Starting from a three-dimensional electro-elastic model with prestrain in the elastic energy, we rigorously derive a reduced plate model in the bending regime. To perform the dimension reduction, that is, to derive the energy of a thin object by taking a suitable limit as its thickness tends to zero, we apply $Γ$-convergence-type methods to the underlying saddle-point problem. In the case of bivariate functionals, this convergence is understood in an adapted epi/hypo-convergence sense. In this concept, we demonstrate the convergence of the rescaled electro-elastic problems to an effective two-dimensional bending model coupled to electric effects. We verify that cluster points of saddle points are saddle points for the limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains Buryachenko, Kateryna Glitzky, Annegret Liero, Matthias Zwicknagl, Barbara Analysis of PDEs 49J45, 74B20, 74K20, 74F15 We study the finite deformation of a thin, elastically heterogeneous sheet subject to electrostatic coupling. The interaction between mechanics and electrostatics is formulated as a saddle-point problem involving the deformation and the electrostatic potential. Starting from a three-dimensional electro-elastic model with prestrain in the elastic energy, we rigorously derive a reduced plate model in the bending regime. To perform the dimension reduction, that is, to derive the energy of a thin object by taking a suitable limit as its thickness tends to zero, we apply $Γ$-convergence-type methods to the underlying saddle-point problem. In the case of bivariate functionals, this convergence is understood in an adapted epi/hypo-convergence sense. In this concept, we demonstrate the convergence of the rescaled electro-elastic problems to an effective two-dimensional bending model coupled to electric effects. We verify that cluster points of saddle points are saddle points for the limit. |
| title | Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains |
| topic | Analysis of PDEs 49J45, 74B20, 74K20, 74F15 |
| url | https://arxiv.org/abs/2511.22320 |