Fu, Y. B., Pearce, S. and Liu, Kuo-Kang (2008) Post-bifurcation analysis of a thin-walled hyperelastic tube under inflation. International Journal of Non-Linear Mechanics, Vol.43 (No.8). pp. 697-706. doi:10.1016/j.ijnonlinmec.2008.03.003

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Abstract

We consider the problem of bulging, or necking, of an infinite thin-walled hyperelastic tube that is inflated by an internal pressure, with the axial stretch at infinity maintained at unity. We present a simple procedure that can be used to derive the bifurcation condition and to determine the near-critical behaviour analytically. It is shown that there is a bifurcation with zero mode number and that the associated axial variation of near-critical bifurcated configurations is governed by a first-order differential equation that admits a locally bulging or necking solution. This result suggests that the corresponding bifurcation pressure can be identified with the so-called initiation pressure which featured in recent experimental studies. This is supported by good agreement between our theoretical predictions and one set of experimental data. It is also shown that the Gent material model can support both bulging and necking solutions whereas the Varga and Ogden material models can only support bulging solutions. Relevance of the present method to the study of non-linear wave propagation in a fluid-filled distensible tube is also discussed.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science, Engineering and Medicine > Engineering > Engineering
Library of Congress Subject Headings (LCSH):	Tubes -- Testing, Stability, Elasticity, Bifurcation theory, Membranes (Biology) -- Mechanical properties
Journal or Publication Title:	International Journal of Non-Linear Mechanics
Publisher:	Pergamon
ISSN:	0020-7462
Official Date:	October 2008
Dates:	Date Event October 2008 Published
Volume:	Vol.43
Number:	No.8
Number of Pages:	10
Page Range:	pp. 697-706
DOI:	10.1016/j.ijnonlinmec.2008.03.003
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	BB/D014786/1 (BBSRC, EPSRC)

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