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Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon

Fu, YB; Xie, YX

Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon Thumbnail


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
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

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