Curvature Potential Formulation for Thin Elastic Sheets
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909941615296512 |
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| author | Cohen, Yael Pandey, Animesh Zhang, Yafei Maor, Cy Moshe, Michael |
| author_facet | Cohen, Yael Pandey, Animesh Zhang, Yafei Maor, Cy Moshe, Michael |
| contents | Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly nonlinear theories, such as the Foppl-von Karman equations, which require small slopes and fail when deflections become large even if strains remain small. We introduce a methodological progress via a geometric reformulation of thin-sheet elasticity based on a stress potential and a curvature potential. This formulation preserves the structure of the classical equations while extending their validity to nonlinear, multivalued configurations, and geometrically frustrated states. The framework provides a unified description of thin-sheet mechanics in regimes inaccessible to existing theories and opens new possibilities for the study of elastic membranes and two-dimensional materials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_03270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature Potential Formulation for Thin Elastic Sheets Cohen, Yael Pandey, Animesh Zhang, Yafei Maor, Cy Moshe, Michael Soft Condensed Matter Materials Science Mathematical Physics Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly nonlinear theories, such as the Foppl-von Karman equations, which require small slopes and fail when deflections become large even if strains remain small. We introduce a methodological progress via a geometric reformulation of thin-sheet elasticity based on a stress potential and a curvature potential. This formulation preserves the structure of the classical equations while extending their validity to nonlinear, multivalued configurations, and geometrically frustrated states. The framework provides a unified description of thin-sheet mechanics in regimes inaccessible to existing theories and opens new possibilities for the study of elastic membranes and two-dimensional materials. |
| title | Curvature Potential Formulation for Thin Elastic Sheets |
| topic | Soft Condensed Matter Materials Science Mathematical Physics |
| url | https://arxiv.org/abs/2512.03270 |