Acta Mech. Sin., 2012, Volume 28, Issue 4, Pages 1209–1218
Stability of aneurysm solutions in a fluid-filled elastic membrane tube
A. T. Il'icheva, Y. B. Fub
a Steklov Mathematical Institute,
Gubkina Str. 8, 119991 Moscow, Russia
b Department of Mathematics,
Keele University, Staffordshire ST5 5BG, U.K.
When a hyperelastic membrane tube is inflated by an internal pressure, a localized bulge will form when the pressure reaches a critical value. As inflation continues the bulge will grow until it reaches a maximum size after which it will then propagate in both directions to form a hat-like profile. The stability of such bulging solutions has recently been studied by neglecting the inertia of the inflating fluid and it was shown that such bulging solutions are unstable under pressure control. In this paper we extend this recent study by assuming that the inflation is by an inviscid fluid whose inertia we take into account in the stability analysis. This reflects more closely the situation of aneurysm formation in human arteries which motivates the current series of studies. It is shown that fluid inertia would significantly reduce the growth rate of the unstable mode and thus it has a strong stabilizing effect.
|Russian Foundation for Basic Research
|This work is supported by a Joint Project
Grant Awarded by the Royal Society and Russian Foundation
for Basic Science Research.
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