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<p>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 <i>h</i>, 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 [Bella &amp; Kohn, Philos. Trans. Roy. Soc. A 2017] to the physically relevant case of a liquid substrate.</p>

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Wrinkling of an elastic sheet floating on a liquid sphere

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Peter Bella,
  • Carlos Román

摘要

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 [Bella & Kohn, Philos. Trans. Roy. Soc. A 2017] to the physically relevant case of a liquid substrate.