Acta Mechanica Solida Sinica

, Volume 25, Issue 2, pp 144–151

# Finite Deformation of a Class of Rectangular Rubber Rings Subjected to end Axial Loads

• Wenzheng Zhang
• Xuegang Yuan
• Hongwu Zhang
• Jiusheng Ren
Article

## Abstract

The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical model is formulated by using the nonlinear field theory and the implicit analytical solutions are derived. Then numerical simulations are implemented to further illustrate the results and obtain some meaningful conclusions. The deformation of the lateral surface of the ring becomes larger with the increasing axial loads, the decreasing ratio of the inner and outer radii and the increasing height of the ring.

## Key words

neo-Hookean material rectangular rubber ring axial load finite deformation implicit analytical solution

## References

1. [1]
Beatty, M.F., Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues—with examples. Applied Mechanics Review, 1987, 40(12): 1699–1735.
2. [2]
Horgan, C.O. and Polignone, D.A., Cavitation in nonlinearly elastic solids: A review. Applied Mechanics Review, 1995, 48(8): 471–485.
3. [3]
Attard, M.M., Finite strain-isotropic hyperelasticity. International Journal of Solids and Structures, 2003, 40(17): 4353–4378.
4. [4]
Fu, Y.B. and Ogden, R.W., Nonlinear Elasticity. Cambridge University Press, 2001.Google Scholar
5. [5]
George, A.F., Strozzi, A. and Rich, J.I., Stress fields in a compressed unconstrained elastomeriv O-ring seal and a comparison of computer predictions with experimental results. Tribology International, 1987, 20(5): 237–247.
6. [6]
Dragoni, E. and Strozzi, A., Analysis of an unpressurized, laterally restrained, elastomeric O-ring seal. Journal of Tribology, 1988, 110(2): 193–200.
7. [7]
Dragoni, E. and Strozzi, A., Theoretical analysis of an unpressurized elastomeric O-ring seal into a rectangular groove. Wear, 1989, 130(1): 41–51.
8. [8]
Nikas, G.K., Elastohydrodynamics and mechanics of rectangular elastomeric seals for reciprocating piston rods. Journal of Tribology, 2003, 125(1): 60–69.
9. [9]
Nikas, G.K. and Sayles, R.S., Nonlinear elasticity of rectangular elastomeric seals and its effect on elastohydrodynamic numerical analysis. Tribology International, 2004, 37(8): 651–660.
10. [10]
Yu, L.W., One kind of fixed seals—quad seal. Fluid Power Transmission and Control, 2006, 16(3): 44–46.
11. [11]
Tan, J., Yang, W.M. and Ding, Y.M., Finite element analysis of rectangular rubber seals. Lubrication Engineering, 2007, 32(2): 36–39.Google Scholar
12. [12]
Truesdell, C. and Noll, W., Nonlinear field theories of mechanics. In: Handbuch der Physik, Bd. III/3, Spriger, Berlin, 1965.Google Scholar
13. [13]
Dai, H.H. and Bi, Q.S., Exact solutions for the large axially symmetric deformations of a neo-hookean rod subjected to static loads. The Quarterly Journal of Mechanics and Applied Mathematics, 2001, 54(1): 39–56.
14. [14]
Chou-Wang, M.S. and Horgan, C.O., Void nucleation and growth for a class of incompressible nonlinearly elastic materials: An example. International Journal of Solids and Structures, 1989, 25(11): 1239–1254.

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

## Authors and Affiliations

• Wenzheng Zhang
• 1
• Xuegang Yuan
• 1
• 2
• Hongwu Zhang
• 1
• Jiusheng Ren
• 3
1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and MechanicDalian University of TechnologyDalianChina
2. 2.School of ScienceDalian National UniversityDalianChina
3. 3.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina