ArticleProceedings. Mathematical, physical, and engineering sciences2017
Indentation of a floating elastic sheet: geometry versus applied tension.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Gigantic floating leaves occupy a large surface area at an economical material cost.Science advances · 2022Article
- Validity of Winkler's mattress model for thin elastomeric layers: beyond Poisson's ratio.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Static bistability of spherical caps.Proceedings. Mathematical, physical, and engineering sciences · 2018Article
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Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force-indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations, the force-indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.
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