How far does a fold go?
How far does a fold go?
We assess the spatial spread of a fold within a narrow elastic strip theoretically and computationally in the small deflection regime. We consider a hierarchy of folding-response ansatz, suitable for stretch-free deformation. The role of Poisson’s coupling between the two curvatures, and that of surface twist, is brought out. Here we show that there exists a critical Poisson’s ratio separating the regime of monotonically decaying fold profiles from that of decaying oscillatory folds. A spatially separable solution results in length-wise localised folds, the length scale of which is in excellent agreement with that obtained from simulations. The persistence length shows significant sensitivity to the Poisson’s ratio of the material. We also establish a mathematical analogy of the folding problem, with one of elastic structures on foundations, the restoring force being proportional to local deflection as well as shear in the foundation.
Folds, Persistence, Poisson effect, Soft elastic sheets
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Jose, Kevin
62171012-92ec-4338-91a4-94b45cdd8645
May 2021
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Jose, Kevin
62171012-92ec-4338-91a4-94b45cdd8645
Abstract
We assess the spatial spread of a fold within a narrow elastic strip theoretically and computationally in the small deflection regime. We consider a hierarchy of folding-response ansatz, suitable for stretch-free deformation. The role of Poisson’s coupling between the two curvatures, and that of surface twist, is brought out. Here we show that there exists a critical Poisson’s ratio separating the regime of monotonically decaying fold profiles from that of decaying oscillatory folds. A spatially separable solution results in length-wise localised folds, the length scale of which is in excellent agreement with that obtained from simulations. The persistence length shows significant sensitivity to the Poisson’s ratio of the material. We also establish a mathematical analogy of the folding problem, with one of elastic structures on foundations, the restoring force being proportional to local deflection as well as shear in the foundation.
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Accepted/In Press date: 27 February 2021
e-pub ahead of print date: 8 March 2021
Published date: May 2021
Additional Information:
Funding Information:
Useful comments on an early draft, by our colleague Professor Neil Stephen, are gratefully acknowledged. We thank Ishaan Manav for assisting us with images in Fig. 1 and their processing.
Publisher Copyright:
© 2021 Elsevier Ltd
Keywords:
Folds, Persistence, Poisson effect, Soft elastic sheets
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Local EPrints ID: 447478
URI: http://eprints.soton.ac.uk/id/eprint/447478
PURE UUID: 69ff1abe-b836-4a22-9f2d-c117c7c64ebb
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Date deposited: 12 Mar 2021 17:31
Last modified: 17 Mar 2024 06:24
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Author:
Kevin Jose
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