Wrinkling of an elastic sheet floating on a liquid sphere
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915802664402944 |
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| author | Bella, Peter Román, Carlos |
| author_facet | Bella, Peter Román, Carlos |
| contents | A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. This generalizes the previous work [P. Bella and R.V. Kohn. Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15504 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wrinkling of an elastic sheet floating on a liquid sphere Bella, Peter Román, Carlos Analysis of PDEs Mathematical Physics A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. This generalizes the previous work [P. Bella and R.V. Kohn. Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate. |
| title | Wrinkling of an elastic sheet floating on a liquid sphere |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2306.15504 |