Analytical solutions for inflation of pre-stretched elastomeric circular membranes under uniform pressure
Analytical solutions for inflation of pre-stretched elastomeric circular membranes under uniform pressure
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预拉伸弹性圆膜在均匀压力下膨胀的解析解
DOI：
10.1016/j.taml.2021.100243
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发表时间：
2021-04
影响因子：
3.4
通讯作者：
Yin Huang
中科院分区：
文献类型：
--
作者：
Jianghong Yuan;Xianlin Liu;Haibin Xia;Yin Huang
弹性体膜经常用于软机器人和柔性电子学等新兴领域。为了便于结构设计，寻找简单的解析解来描述它们在外载作用下的弹性变形是非常有吸引力的。然而，由于材料/几何非线性和边界约束引起的变形不均匀，使得得到精确的解析解变得非常困难。本文研究了预拉伸弹性圆膜在均匀压力下的充气问题，在对充气膜形状进行合理假设的基础上，推导出了压力-体积曲线的近似解析解。这样的显式表达式使我们能够定量地设计预拉伸膜的材料和几何参数，以产生具有给定的峰值和初始斜率的目标压力-体积曲线。这项工作将有助于包括弹性膜的结构的简化机械设计。
Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics. For convenience of the structural design, it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings. However, both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution. In this paper, we focus on the inflation of a pre-stretched elastomeric circular membrane under uniform pressure, and derive an approximate analytical solution of the pressure–volume curve based upon a reasonable assumption on the shape of the inflated membrane. Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure–volume curve with prescribed peak point and initial slope. This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.
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