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We consider localised bulging/necking in an inflated hyperelastic membranetube with closed ends. We first show that the initiation pressure for the onsetof localised bulging is simply the limiting pressure in uniform inflation whenthe axial force is held fixed. We then demonstrate analytically how, asinflation continues, the initial bulge grows continually in diameter until itreaches a critical size and then propagates in both directions. The bulgingsolution before propagation starts is of the solitary-wave type, whereas thepropagating bulging solution is of the kink-wave type. The stability, withrespect to axially symmetric perturbations, of both the solitary-wave type andthe kink-wave type solutions is studied by computing the Evans function usingthe compound matrix method. It is found that when the inflation ispressure-controlled, the Evans function has a single non-negative real root andthis root tends to zero only when the initiation pressure or the propagationpressure is approached. Thus, the kink-wave type solution is probably stablebut the solitary-wave type solution is definitely unstable.

Characterisation and stability of localised bulging/necking in inflated membrane tubes