A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness
A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness
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DOI：
10.1016/j.jmps.2023.105276
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发表时间：
2023-01
影响因子：
5.3
通讯作者：
Xiang Yu;Yibin Fu
中科院分区：
文献类型：
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作者：
Xiang Yu;Yibin Fu
通过应用Audoly和哈钦森（2016）提出的降维方法，我们从三维（3d）有限弹性理论推导出一个一维（1d）模型，用于分析无限壁厚的膨胀超弹性管中的膨胀或颈缩。一维模型使得它更容易表征完全非线性轴对称变形的厚壁管使用简单的数值方案，如有限差分法。新模型恢复了用于分析膜管中鼓出的扩散界面模型和用于研究拉伸固体圆柱中颈缩的一维模型作为两种极限情况。它是一致的，但显着细化，精确的线性和弱非线性分岔分析。与有限元模拟的比较表明，对于胀形问题，一维模型能够准确地描述整个胀形过程，从启动，增长，到传播。一维模型提供了一个垫脚石，从类似的一维模型可以导出和用于研究其他效应，如各向异性和电负荷，以及其他现象，如破裂。
We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube offinite wall thicknessfrom 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.