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

TL;DR

This paper develops a simplified one-dimensional model for analyzing axisymmetric deformations like bulging and necking in inflated hyperelastic tubes with finite wall thickness, making complex nonlinear analysis more accessible.

Contribution

It introduces a new 1d model derived from 3d elasticity theory that accurately captures nonlinear deformations and improves upon existing models for thick-walled hyperelastic tubes.

Findings

The 1d model accurately describes the entire bulging process.

It recovers existing models as special cases.

The model aligns well with finite element simulations.

Abstract

We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube of {\it finite wall thickness} from the three-dimensional 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 axisymmetric 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 problem, 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.