Stability of localized bulging in inflated membrane tubes under volume control

We study the stability of localized bulging solutions in an inflated hyperelastic membrane tube using an energy stability criterion. We first use this criterion to confirm a previously known result obtained using a dynamic stability criterion, namely that under pressure control all such bulging solutions are unstable. It is then shown that, under volume control, the solutions in the early stages of bulging are unstable whereas those in the later stages of bulging are stable. To be more precise, it is found that the unstable solutions correspond exactly to the snap-back section of the associated pressure–volume diagram.