Prevention of localized bulging in an inflated bilayer tube

Abstract

This paper studies the bifurcation behavior in an inflated bilayer tube of arbitrary thickness under inflation and uni-axial extension. It is assumed that both layers are composed of the Gent material with each layer having its own Jm, where Jm is a material parameter in the Gent model that signifies the maximum extensibility. First, we determine several critical parametrical regions where localized bulging disappears for a single-layer tube. Then we investigate localized bulging in an inflated bilayer tube, where one layer (layer I) of the tube cannot bulge whereas the other part (layer II) can. Surprisingly, we find that such a composite tube is still susceptible to localized bulging and localized bulging can be prevented only if the proportion of layer I exceeds a critical value, no matter whether layer I occupies the inner side or the outer side. Even for a very thin bilayer tube, the same feature holds. The cases of fixed axial force and fixed axial stretch are both studied, and the critical geometrical parameters marking the transition between bulging and no bulging are determined. Moreover, we carry out a numerical analysis by use of the finite element method to verify the applicability of an explicit bifurcation condition and the predicted bifurcation behavior. This paper offers a possible way to avoid bulging formation in a cylindrical tube while retaining moderate extensibility.