We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube of finite wall thickness from the three-dimensional (3d) finite elasticity theory by applying the dimension reduction methodology proposed by Audoly and Hutchinson (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.

我们推导了一个一维 (1d) 模型，用于分析有限壁厚的充气超弹性管中的膨胀或颈缩通过应用 Audoly 和 Hutchinson (2016) 提出的降维方法，从三维 (3d) 有限弹性理论得出。一维模型可以更轻松地使用有限差分法等简单的数值方案来表征厚壁管的完全非线性轴对称变形。新模型恢复了用于分析膜管膨胀的扩散界面模型和用于研究拉伸实心圆柱体颈缩的一维模型作为两个极限情况。它与精确的线性和弱非线性分岔分析一致，但显着改进。与有限元模拟的比较表明，对于膨胀问题，一维模型能够准确地描述整个膨胀过程，从开始、增长到传播。