Journal article
Viscoelastic ribbons
- Abstract:
- A reduced model is presented for the dynamics of a slender sheet of a viscoelastic fluid. Starting with the Oldroyd-B constitutive model and exploiting an asymptotic analysis in the small aspect ratio of the sheet, equations are derived for the evolution of a ‘visco-elastica’. These depend on an elastic modulus, a creep viscosity and a solvent viscosity. They resemble standard equations for an elastica or a viscida, to which they reduce under the appropriate limits. The model is used to explore the effects of viscoelasticity on the dynamics of a curling ribbon, a drooping cantilever, buckling sheets, snap-through and a falling catenary. We then incorporate a yield stress, for a fluid that deforms by creep only above a critical stress, revisiting the curling and cantilever problems. This model generalises a number of previous theories for viscoelastic and viscoplastic ribbons.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 1.4MB, Terms of use)
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- Publisher copy:
- 10.1017/jfm.2020.870
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Journal of Fluid Mechanics More from this journal
- Volume:
- 908
- Article number:
- A5
- Publication date:
- 2020-12-03
- Acceptance date:
- 2020-09-24
- DOI:
- EISSN:
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1469-7645
- ISSN:
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0022-1120
- Language:
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English
- Keywords:
- Pubs id:
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1147825
- Local pid:
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pubs:1147825
- Deposit date:
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2020-12-03
- ARK identifier:
Terms of use
- Copyright holder:
- Hewitt and Balmforth.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s), 2020. Published by Cambridge University Press
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Cambridge University Press at: https://doi.org/10.1017/jfm.2020.870
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