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Analysis and computations for a model of quasi-static deformation of a thinning sheet arising in superplastic forming

journal contribution
posted on 2023-06-07, 13:52 authored by K Deckelnick, Charles Martin Elliott, Vanessa StylesVanessa Styles
We consider a mathematical model for the quasi-static deformation of a thinning sheet. The model couples a first-order equation for the thickness of the sheet to a prescribed curvature equation for the displacement of the sheet. We prove a local in time existence and uniqueness theorem for this system when the sheet can be written as a graph. A contact problem is formulated for a sheet constrained to be above a mould. Finally we present some computational results.

History

Publication status

  • Published

Journal

European Journal of Applied Mathematics

ISSN

0956-7925

Issue

04

Volume

13

Page range

403-429

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2007-03-16

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