The effect of residual stress on the stability of a circular cylindrical tube

Dorfmann, L. and Ogden, R. W. (2021) The effect of residual stress on the stability of a circular cylindrical tube. Journal of Engineering Mathematics, 127, 9. (doi: 10.1007/s10665-021-10097-4)

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Residual stresses in an unloaded configuration of an elastic material have a significant influence on the response of the material from that configuration, but the effect of residual stress on the stability of the material, whether loaded or unloaded, has only been addressed to a limited extent. In this paper we consider the level of residual stress that can be supported in a thick-walled circular cylindrical tube of non-linearly elastic material without loss of stability when subjected to fixed axial stretch and either internal or external pressure. In particular, we consider the tube to have radial and circumferential residual stresses, with a simple form of elastic constitutive law that accommodates the residual stress, and incremental deformations restricted to the cross section of the tube. Results are described for a tube subject to a level of (internal or external) pressure characterized by the internal azimuthal stretch. Subject to restrictions imposed by the strong ellipticity condition, the emergence of bifurcated solutions is detailed for their dependence on the level of residual stress and mode number.

Item Type:Articles
Additional Information:A correction to this article is available at
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Dorfmann, L., and Ogden, R. W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Engineering Mathematics
ISSN (Online):1573-2703
Published Online:04 March 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Journal of Engineering Mathematics 127: 9
Publisher Policy:Reproduced under a Creative Commons License
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