Fu, YB and Xie, YX (2014) Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon. Journal Of The Mechanics And Physics Of Solids, 68. 33 - 44.

[img]
Preview
Text
sphere-v4.pdf - Accepted Version

Download (208kB) | Preview

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.

Item Type: Article
Uncontrolled Keywords: Bifurcation, Stability, Energy criterion, Nonlinear elasticity, Spherical shells
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Related URLs:
Depositing User: Symplectic
Date Deposited: 03 Dec 2015 15:24
Last Modified: 20 May 2019 08:15
URI: http://eprints.keele.ac.uk/id/eprint/1269

Actions (login required)

View Item View Item