Localized bulging in an inflated hyperelastic tube: the effects of rotation, multi-layering and torsion

Abstract

In this thesis, we start by considering a hyperelastic circular solid cylinder or tube that is rotating about its axis of symmetry with angular velocity ω. If the resultant axial force F is fixed, it is shown that the bifurcation condition for a solid cylinder or a tube that is shrink-fitted to a rigid circular cylindrical spindle is simply given by dω/dλz = 0, where λz is the axial stretch. When the spindle is absent (the case of unconstrained rotation), we also allow for the possibility that the tube is additionally subjected to an internal pressure P. It is shown that with P fixed, and ω and F both viewed as functions of the circumferential stretch λa and λz, the bifurcation condition for localized bulging is that the Jacobian of ω and F should vanish. The second part of the thesis studies localized bulging in an inflated bilayer tube under inflation and axial extension. Firstly, bulging prevention in a hyperelastic bilayer tube composed of the Gent material is investigated. We determine several critical parameter regimes where localized bulging disappears, when one layer (layer I) of the tube cannot bulge whereas the other part (layer II) can. Surprisingly, we find that localized bulging still occurs if the proportion of layer II exceeds a critical value, no matter whether it occupies the inner layer or outer layer. Secondly, we focus on the effect of modulus ratio between two layers on the bulge formation. If the thickness of the bilayer tube is specified, the composite tube is more stable when the stiffer part occupies the outer layer. Moreover, the critical volume ratio vcr as a function of the interfacial radius D has a maximum if s > 1 but a minimum if s > 1 but a minimum if s < 1, where s is the ratio of the shear modulus of the outer layer to that of the inner layer. Finally, we turn our attention to study the effect of torsion on the onset of localized bulging. When the twisting moment M is fixed, the bifurcation condition for localized bulging is that the Jacobian of the internal pressure P and the resultant axial force F should vanish. It is found that the onset of localized bulging can be delayed or removed when a torsion is applied to the tube.