ArticleProceedings. Mathematical, physical, and engineering sciences2017
Curvature-driven morphing of non-Euclidean shells.
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 5 papers.
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Who cites it
5 citing papers in PubMed.
- Temporal and spatial patterns of leaf unrolling inJournal of biosciences · 2026Article
- Curvature-driven instabilities in thin active shells.Royal Society open science · 2022Article
- Morphoelasticity of large bending deformations of cell sheets during development.Physical review. E · 2021Article
- Helical Structures Mimicking Chiral Seedpod Opening and Tendril Coiling.Sensors (Basel, Switzerland) · 2018Review
- 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
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.
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Registered trials
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