Abstract
Invaginations are partial enclosures formed by surfaces. Typically formed by biological membranes; they abound in nature. In this paper, we consider fundamentally different structures: elastically stabilized invaginations. Focusing on spherical invaginations formed by elastic membranes, we carried out experiments and mathematical modeling to understand the stress and strain fields underlying stable structures. Friction plays a key role in stabilization, and consequently the required force balance is an inequality. Using a novel scheme, we were able to find stable solutions of the balance equations for different models of elasticity, with reasonable agreement with experiments.
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Notes
The modulus and thickness of the membranes were measured by us.
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Acknowledgements
This work was supported by the Office of Naval Research through the MURI on Photomechanical Material Systems (ONR N00014-18-1-2624).
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Zheng, X., Guo, T. & Palffy-Muhoray, P. An Elastically Stabilized Spherical Invagination. J Elast 153, 723–733 (2023). https://doi.org/10.1007/s10659-022-09927-y
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DOI: https://doi.org/10.1007/s10659-022-09927-y