Extension, inflation and torsion of a residually-stressed circular cylindrical tube

Merodio, J. and Ogden, R. W. (2016) Extension, inflation and torsion of a residually-stressed circular cylindrical tube. Continuum Mechanics and Thermodynamics, 28(1), pp. 157-174. (doi:10.1007/s00161-015-0411-z)

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Abstract

In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Merodio, J., and Ogden, R. W.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Continuum Mechanics and Thermodynamics
Publisher:Springer Berlin Heidelberg
ISSN:0935-1175
ISSN (Online):1432-0959
Published Online:25 January 2015
Copyright Holders:Copyright © 2015 Springer-Verlag
First Published:First published in Continuum Mechanics and Thermodynamics 28(1): 157-174
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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