Pearce, SP and Fu, YB (2010) Characterization and stability of localized bulging/necking in inflated membrane tubes. IMA Journal of Applied Mathematics, 75 (4). 581 - 602. ISSN 1464-3634

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Characterisation and stability of localised bulging-necking in inflated membrane tubes (YFu).pdf

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We consider localized bulging/necking in an inflated hyperelastic membrane tube with closed ends. We first show that the initiation pressure for the onset of localized bulging is simply the limiting pressure in uniform inflation when the axial force is held fixed. We then demonstrate analytically how, as inflation continues, the initial bulge grows continually in diameter until it reaches a critical size and then propagates in both directions. The bulging solution before propagation starts is of the solitary-wave type, whereas the propagating bulging solution is of the kink-wave type. The stability, with respect to axially symmetric perturbations, of both the solitary-wave type and the kink-wave type solutions is studied by computing the Evans function using the compound matrix method. It is found that when the inflation is pressure controlled, the Evans function has a single non-negative real root and this root tends to zero only when the initiation pressure or the propagation pressure is approached. Thus, the kink-wave type solution is probably stable but the solitary-wave type solution is definitely unstable.

Item Type: Article
Uncontrolled Keywords: tube inflation; aneurysm; non-linear elasticity; stability; bifurcation
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 20 Nov 2014 15:49
Last Modified: 11 Jun 2019 15:05

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