一种用于分析膨胀超弹性管轴对称变形的一维模型
A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness
AI总结：
本文提出了一种用于分析膨胀超弹性管轴对称变形的一维模型，该模型通过降维方法推导，能够有效描述厚壁管的非线性变形及隆起过程。
摘要：
我们通过应用Audoly和Hutchinson（J. Mech. Phys. Solids, 97, 2016）提出的一维降维方法，从三维有限弹性理论中推导出一个一维（1d）模型，用于分析膨胀超弹性管的隆起或颈缩现象。该一维模型使使用简单的数值方案如有限差分法来完全非线性轴对称变形的厚壁管的表征变得 much 更加容易。新模型恢复了分析膜管隆起的扩散界面模型和研究拉伸固体圆柱颈缩的一维模型作为两个极限情况。它与但显著改进了精确线性和弱非线性分叉分析。与有限元模拟的比较表明，对于隆起问题，该一维模型能够准确描述整个隆起过程，从起始、增长到传播。该一维模型为推导和用于研究其他效应如各向异性和电加载，以及其他现象如破裂的类似一维模型提供了基础。
英文摘要：
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.
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