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When a hyperelastic membrane tube is inflatedby an internal pressure, a localized bulge will form when thepressure reaches a critical value. As inflation continues thebulge will grow until it reaches a maximum size after whichit will then propagate in both directions to form a hat-likeprofile. The stability of such bulging solutions has recentlybeen studied by neglecting the inertia of the inflating fluidand it was shown that such bulging solutions are unstableunder pressure control. In this paper we extend this recentstudy by assuming that the inflation is by an inviscid fluidwhose inertia we take into account in the stability analysis.This reflects more closely the situation of aneurysm forma-tion in human arteries which motivates the current series ofstudies. It is shown that fluid inertia would significantly re-duce the growth rate of the unstable mode and thus it has astrong stabilizing effect.
When a hyperelastic membrane tube is inflatedby an internal pressure, a localized bulge will form when thepressure reaches a maximum value after whichit will then propagate in both both to form a hat-likeprofile. The stability of such bulging solutions has recentlybeen studied by neglecting the inertia of the inflating fluid and it was shown that asse bulging solutions are unstableunder pressure control. In this paper we extend this recent study by assuming that the inflation is by an inviscid fluidwhine inertia we take into account in the stability analysis. This reflects more closely the situation of aneurysm forma-tion in human arteries which motivates the current series of systems. It is shown that fluid inertia would significantly re-duce the growth rate of the unstable mode and thus it has astrong stabilizing effect