Effects of imperfections on localized bulging in inflated membrane tubes

The problem of localized bulging in inflated membrane tubes shares the same features with a variety of other localization problems such as formation of kink bands in fibre-reinforced composites and layered structures. This type of localization is known to be very sensitive to imperfections, but the precise nature of such sensitivity has not so far been quantified. In this paper, we study effects of localized wall thinning/thickening on the onset of localized bulging in inflated membrane tubes as a prototypical example. It is shown that localized wall thinning may reduce the critical pressure or circumferential stretch by an amount of the order of the square root of maximum wall thickness reduction. As a typical example, a 10 per cent maximum wall thinning may reduce the critical circumferential stretch by 19 per cent. This square root law complements the well-known Koiter's two-thirds power law for subcritical periodic bifurcations. The relevance of our results to mathematical modelling of aneurysm formation in human arteries is also discussed.