Yibin Fu y.fu@keele.ac.uk
Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon
Fu, YB; Xie, YX
Authors
YX Xie
Abstract
It is well-known that for most spherical rubber balloons the pressure versus volume curve associated with uniform inflation is N-shaped (the pressure increases rapidly to a maximum, falls to a minimum, and subsequently increases monotonically), and that somewhere along the descending branch of this curve the spherical shape may bifurcate into a pear shape through localized thinning near one of the poles. The bifurcation is associated with the (uniform) surface tension reaching a maximum. It is previously known that whenever a pear-shaped configuration becomes possible, it has lower energy than the co-existing spherical configuration, but the stability of the pear-shaped configuration itself is unknown. With the use of the energy stability criterion, it is shown in this paper that the pear-shaped configuration is unstable under pressure control, but stable under mass control. Our calculations are carried out using the Ogden material model as an example, but it is expected that the qualitative stability results should also be valid for other material models that predict a similar N-shaped behavior for uniform inflation.
Acceptance Date | Mar 13, 2014 |
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Publication Date | Mar 26, 2014 |
Publicly Available Date | Mar 29, 2024 |
Journal | Journal Of The Mechanics And Physics Of Solids |
Print ISSN | 0022-5096 |
Publisher | Elsevier |
Pages | 33 - 44 |
DOI | https://doi.org/10.1016/j.jmps.2014.03.007 |
Keywords | Bifurcation, Stability, Energy criterion, Nonlinear elasticity, Spherical shells |
Publisher URL | https://doi.org/10.1016/j.jmps.2014.03.007 |
Files
sphere-v4.pdf
(208 Kb)
PDF
Publisher Licence URL
https://creativecommons.org/licenses/by-nc-nd/4.0/
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