Finite inflation of an initially stretched hyperelastic circular membrane
Finite inflation of an initially stretched hyperelastic circular membrane
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DOI：
10.1016/j.euromechsol.2013.02.007
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发表时间：
2013-09
影响因子：
4.1
通讯作者：
Amit Patil;A. Dasgupta
中科院分区：
文献类型：
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作者：
Amit Patil;A. Dasgupta
本文分析了初始拉伸平面圆超弹性膜的有限轴对称膨胀问题。膜材料被认为是均匀的、各向同性的Mooney-Rivlin固体。膨胀问题已被简化为使用一组适当定义的变量的三个一阶常微分方程的集合。利用这些方程对尺度的不变性，提出了一种求解两点边值问题的简便方法。这种方法不需要任何特殊的技术来协商膜的压力-拉伸关系的极限点。得到了不同材料参数下初始未拉伸和预拉伸圆膜的几种膨胀结果。明确了预拉伸和内部压力在膨胀机制中的作用。最初的拉伸被观察到对膜的膨胀有一些有趣的反直觉的影响。
In this paper, finite axisymmetric inflation of an initially stretched flat circular hyperelastic membrane has been analyzed. The membrane material has been assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The inflation problem has been reduced to a set of three first order ordinary differential equations using a set of appropriately defined variables. An interesting method based on the invariance of these equations to scaling has been used to solve the two point boundary value problem without much effort. This method does not require any special technique for negotiating the limit points in the pressure–stretch relations of the membrane. Several inflation results of an initially unstretched and pre-stretched circular membrane for various material parameters are obtained. The roles of pre-stretch and internal pressure on the inflation mechanics are clearly delineated. The initial stretch is observed to have some interesting counter-intuitive effects on the inflation of the membrane.