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Ball, Thomasina and Balmforth, Neil J. (2021) Viscoplastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2254). 20210509. doi:10.1098/rspa.2021.0509 ISSN 1471-2946.
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Official URL: https://doi.org/10.1098/rspa.2021.0509
Abstract
An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Library of Congress Subject Headings (LCSH): | Viscoplasticity , Fluid mechanics, Fluid mechanics -- Mathematical models, Plates (Engineering) -- Plastic properties | ||||||||
| Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||||
| Publisher: | The Royal Society | ||||||||
| ISSN: | 1471-2946 | ||||||||
| Official Date: | 27 October 2021 | ||||||||
| Dates: |
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| Volume: | 477 | ||||||||
| Number: | 2254 | ||||||||
| Article Number: | 20210509 | ||||||||
| DOI: | 10.1098/rspa.2021.0509 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 26 October 2021 | ||||||||
| Date of first compliant Open Access: | 26 October 2021 |
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