A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Abstract

We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hy?perelastic tube of finite wall thickness from the three-dimensional (3d) finite elasticity theory by
applying the dimension reduction methodology proposed by Audoly and Hutchinson (J. Mech.
Phys. Solids, 97, 2016). The 1d model makes it much easier to characterize fully nonlinear ax?isymmetric deformations of a thick-walled tube using simple numerical schemes such as the finite
difference method. The new model recovers the diffuse interface model for analyzing bulging in
a membrane tube and the 1d model for investigating necking in a stretched solid cylinder as two
limiting cases. It is consistent with, but significantly refines, the exact linear and weakly nonlinear
bifurcation analyses. Comparisons with finite element simulations show that for the bulging prob?lem, the 1d model is capable of describing the entire bulging process accurately, from initiation,
growth, to propagation. The 1d model provides a stepping stone from which similar 1d models
can be derived and used to study other effects such as anisotropy and electric loading, and other
phenomena such as rupture.