Localized bulging in an inflated bilayer tube of arbitrary thickness: Effects of the stiffness ratio and constitutive model

Abstract

We study a bilayer tube subject to inflation and axial stretching to reveal the effects of s, which is the ratio of the shear modulus of the outer layer to that of the inner layer, the interfacial radius D, and different constitutive models on the bulge initiation. By use of the internal volume ratio v as the bifurcation parameter, a parametric study is carried out. It is found that a larger s produces a more stable bilayer tube. 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 D has a maximum if s > 1 but a minimum if s < 1. We investigate the cases of fixed axial force and fixed axial length using the Gent model and Ogden model. A careful analysis shows that the qualitative characteristic of the variations of vcr with respect to the modulus ratio s and the interfacial radius D is almost insensitive to the constitutive model used. Therefore, the effect of s on the bulge initiation is an intrinsic property of a bilayer tube. Furthermore, the maximum radius of a bulge in the propagation stage is studied when the thickness of the bilayer tube is prescribed. In the case of fixed axial force, analytical results based on Maxwell’s equal-area rule agree well with the corresponding numerical ones by utilizing finite element method. However, for the other loading type, only numerical solutions are available. It turns out that a bilayer tube with a higher vcr can attain a larger bulge in the propagation stage. In particular, the dependence of the maximum radius on D also has a maximum when s > 1 but a minimum otherwise. The current study provides useful insight into aneurysm formation in human arteries and offers a possible way to control bulge initiation using a bilayer tube.