Abstract

The mechanical behavior of a thick-walled pressure vessel composed of an incompressible isotropic nonlinearly elastic material subjected to the combined pressure and extension-torsion loading is investigated. An analytical solution is proposed for the general form of the free strain energy density, and different models including well-known Neo-Hookean, Mooney-Rivlin, and recently presented free energy contained two exponential terms -exp-exp model- which is strongly stable and compatible with experimental data, are employed. Comparing different constitutive models involves compatible calibration for a specific material. Thus, the uniaxial and equi-biaxial experimental data of silicon-rubber are simultaneously considered to be used in a calibration optimization procedure. Regarding the application of extension-torsion problem, e.g., biological application in papillary muscles, it is required to inspect this loading on a hollow cylinder and considering the internal and external pressure make the problem more realistic to be employed as capillary muscle. After proposing a closed-form solution for this problem, the finite element analysis of the same problem is conducted to verify the proposed analytical solution. Comparing the results of non-dimensional stress, force and moment distribution of analytical and finite element methods illustrate excellent agreement which confirms the accuracy of the presented solution. Some designing factors including the value of applied twist, axial stretch and pressure, and radius ratio are studied. Results demonstrate that the exp-exp model is more conservative in a small amount of twist and axial stretch. However, it yields a higher value for the stress, force, and moment in larger twists and stretches.

摘要

研究了由不可压缩的各向同性非线性弹性材料组成的厚壁压力容器在压力和拉伸-扭转联合载荷作用下的力学行为。对自由应变能密度的一般形式提出了解析解，不同的模型包括著名的 Neo-Hookean、Mooney-Rivlin，以及最近提出的自由能包含两个指数项-exp-exp 模型-这是强稳定的并与实验数据兼容，被采用。比较不同的本构模型涉及特定材料的兼容校准。因此，硅橡胶的单轴和等双轴实验数据被同时考虑用于校准优化过程。关于延伸-扭转问题的应用，例如，在乳头肌中的生物学应用，需要在空心圆柱体上检查这种负载，并考虑内部和外部压力，使问题更适合用作毛细管肌。在对该问题提出封闭形式的解后，对同一问题进行有限元分析，以验证所提出的解析解。比较分析和有限元方法的无量纲应力、力和力矩分布的结果说明了很好的一致性，这证实了所提出的解决方案的准确性。研究了一些设计因素，包括施加的扭曲值、轴向拉伸和压力以及半径比。结果表明，exp-exp模型在少量的扭曲和轴向拉伸下更加保守。然而，