Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube

El Hamdaoui, M., Merodio, J. and Ogden, R. W. (2018) Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube. Journal of Engineering Mathematics, 109(1), pp. 31-45. (doi:10.1007/s10665-017-9904-z)

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Abstract

When a transversely isotropic circular cylindrical tube is subject to axial extension and inflation, the governing equations of equilibrium can lose ellipticity under certain combinations of deformation and direction of transverse isotropy. In this paper, it is shown how the inclusion of an axial shear deformation moderates the loss of ellipticity condition. In particular, this condition is analysed for a material model consisting of an isotropic neo-Hookean matrix within which are embedded fibres whose properties are characterized by the addition to the strain-energy function of a reinforcing model depending on the local fibre direction.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: El Hamdaoui, M., Merodio, J., and Ogden, R. W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Engineering Mathematics
Publisher:Springer
ISSN:0022-0833
ISSN (Online):1573-2703
Published Online:26 May 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Journal of Engineering Mathematics 109(1):31-45
Publisher Policy:Reproduced under a Creative Commons License

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