Viscoelastic ribbons
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 ela...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Cambridge University Press
2020
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| _version_ | 1797057140014186496 |
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| author | Hewitt, IJ Balmforth, NJ |
| author_facet | Hewitt, IJ Balmforth, NJ |
| author_sort | Hewitt, IJ |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T19:32:03Z |
| format | Journal article |
| id | oxford-uuid:1dc7baf4-0d92-49f6-b8a0-e1f7e0eac452 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:32:03Z |
| publishDate | 2020 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:1dc7baf4-0d92-49f6-b8a0-e1f7e0eac4522022-03-26T11:12:48ZViscoelastic ribbonsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1dc7baf4-0d92-49f6-b8a0-e1f7e0eac452EnglishSymplectic ElementsCambridge University Press2020Hewitt, IJBalmforth, NJA 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. |
| spellingShingle | Hewitt, IJ Balmforth, NJ Viscoelastic ribbons |
| title | Viscoelastic ribbons |
| title_full | Viscoelastic ribbons |
| title_fullStr | Viscoelastic ribbons |
| title_full_unstemmed | Viscoelastic ribbons |
| title_short | Viscoelastic ribbons |
| title_sort | viscoelastic ribbons |
| work_keys_str_mv | AT hewittij viscoelasticribbons AT balmforthnj viscoelasticribbons |