ArticleProceedings. Mathematical, physical, and engineering sciences2018
Static bistability of spherical caps.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- Dimple-Encoded Reprogrammable Origami.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Deployable 3D architectures from wafer-fabricated precursors.Nature communications · 2026Article
- Remorphable Architectures: Reprogramming Global Bistability through Locally Bistable Metamaterials.Advanced materials (Deerfield Beach, Fla.) · 2026Article
- Coaxial Direct Ink Writing of Cholesteric Liquid Crystal Elastomers in 3D Architectures.Advanced materials (Deerfield Beach, Fla.) · 2025Article
- Bistable Soft Shells for Programmable Mechanical Logic.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Leaping liquid crystal elastomers.Science advances · 2023Article
- Curvature-driven instabilities in thin active shells.Royal Society open science · 2022Article
- Efficient snap-through of spherical caps by applying a localized curvature stimulus.The European physical journal. E, Soft matter · 2022Article
- Universally bistable shells with nonzero Gaussian curvature for two-way transition waves.Nature communications · 2021Article
- Dome-Patterned Metamaterial Sheets.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2020Article
- Bistable polar-orthotropic shallow shells.Royal Society open science · 2019Article
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Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two 'self-equilibrated' states, one natural and the other inside out (or 'everted'). Though this is familiar from everyday life-an umbrella is remarkably stable, yet a contact lens can be easily turned inside out-the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more 'robust' to snap-through. Our work sheds new light on the robustness of the 'mirror buckling' symmetry of spherical shell caps.
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