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Viscoplastic plates

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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

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Official URL: https://doi.org/10.1098/rspa.2021.0509

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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
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Faculty of 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:
DateEvent
27 October 2021Published
13 October 2021Available
9 September 2021Accepted
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

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