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Post-bifurcation analysis of a thin-walled hyperelastic tube under inflation
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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 ISSN 0020-7462.
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Official URL: http://dx.doi.org/10.1016/j.ijnonlinmec.2008.03.00...
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 | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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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: |
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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) |
Data sourced from Thomson Reuters' Web of Knowledge
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