Stability of aneurysm solutions in a fluid-filled elastic membrane tube

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.     

Study of bifurcation in a pressurized hyperelastic membrane tube enclosed by a soft substrate

We model a perivascular supported arterial tube as a uniform cylindrical membrane tube enclosed by a soft substrate, and derive the solution bifurcation criterion. We assume the surrounding soft substrate as an elastic foundation with distributed stiffness. We consider the tube to be a neo-Hookean material with isotropic and anisotropic (orthotropic) properties, and study solution bifurcation at a constant axial stretch. In the isotropic case, the surrounding soft substrate can substantially delay the onset of bifurcation through a subcritical jump in circular distension at bifurcation with increasing substrate stiffness. Introduction of anisotropy can significantly change the jump behavior from subcritical to supercritical.