Earthquake Engineering and Engineering Vibration

, Volume 16, Issue 4, pp 815–826 | Cite as

Development of a modified Mooney-Rivlin constitutive model for rubber to investigate the effects of aging and marine corrosion on seismic isolated bearings

  • Guifeng Zhao
  • Yuhong Ma
  • Yanmin Li
  • Jiarun Luo
  • Chang Du
Technical Papers


In this study, aging and marine corrosion tests of a large number of rubber material and rubber bearings have been carried out. The constitutive Mooney-Rivlin model parameters for a rubber isolated bearing have been determined. By applying the least-square method to the experimental data, the relationships between the aging time and the marine corrosion time with the constants in the constitutive model for a rubber bearing have been derived. Next, the Mooney-Rivlin model has been modified accordingly. Further, using the modified Mooney-Rivlin model and the Abaqus software, the performance of the rubber isolated bearings has been simulated. The simulation results have been compared to the experimental results so as to verify the accuracy of the modified model. The comparison shows that the maximum errors for the vertical and horizontal stiffnesses are 16.8% and 0.49%, respectively. Since these errors are considered acceptable, the accuracy of the modified constitutive model can be considered verified. The results of this study can provide theoretical support for the performance study on rubber isolated bearings under the complex ocean environment and the life-cycle performance evaluation of bridges and other offshore structures.


isolated rubber bearing marine corrosion aging Mooney-Rivlin model finite element analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Boyce MC and Arruda EM (2000), “Constitutive Models of Rubber Elasticity: A Review,” Rubber Chemistry and Technology, 73(3): 504–523.CrossRefGoogle Scholar
  2. Bu Jiling and Huang Youjian (2010), The Calculation Algorithm for the Rubber Elastic Element Design of the Railway Vehicle, Beijing: China Railway Publishing House. (in Chinese)Google Scholar
  3. Chao-Hsun Chen and Yu-Chung Wang (1997), “An Extended Nonlinear Mechanical Model for Solid-filled Mooney-rivlin Rubber Composites,” Polymer, 38(3): 571–576.CrossRefGoogle Scholar
  4. Ha-Anh T and Vu-Khanh T (2005), “Prediction of Mechanical Properties of Polychloroprene during Thermo-oxidative Aging,” Polymer Testing, 24(6): 775–780.CrossRefGoogle Scholar
  5. Huang Jianlong, Xie Guangjuan and Liu Zhengwei (2008), “Finite Element Analysis of Super-elastic Rubber Materials based on the Moony-rivlin and Yeoh Model,” China Rubber /Plastics Technology and Equipment, 34(12): 22–26. (in Chinese)Google Scholar
  6. Huang Qingzhuan (2009), “Rubber Moony-rivlin Model and Its Modulus’s Least-square Solution,” Chinese Journal of Tropical Agriculture, 29(5): 20–24. (in Chinese)Google Scholar
  7. ISO 22762-3, Elastomeric seismic-protection isolators-Part 3: Applications for buildings -Specifications. Liu Meng, Wang Qingqing and Wang Guoquan (2011), “Determination for Material Constants of Rubber Mooney-Rivlin Model,” Rubber Industry, 58(4): 241–245. (in Chinese)Google Scholar
  8. Ma Yuhong, Luo Jia run, Cui Jie et al. (2016), “Performance Deterioration Tests of Rubber Isolators for Offshore Bridges Under Marine Environment,” China Journal of Highway and Transport, 29(2): 52–61. (in Chinese)Google Scholar
  9. Mooney M (1940), “A Theory of Large Elastic Deformation,” Journal of Applied Physics, 11(6): 582–592.CrossRefGoogle Scholar
  10. Mott PH and Roland CM (2001), “Aging of Natural Rubber in Air and Seawater,” Rubber Chemistry and Technology, 74(1): 79–88.CrossRefGoogle Scholar
  11. Namjoo Moslem and Golbakhsseln (2014), “Numerical Simulation of Tire-soil Interaction Using a Verified 3D Finite Element Model,” Journal of Central South University of Technology, 21: 817–821.CrossRefGoogle Scholar
  12. Rivlin R S (1948), “Large Elastic Deformations of Isotropic Materials, II. Some Uniqueness Theorems for Pure, Homogeneous Deformation,” Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, 240(822): 491–508.CrossRefGoogle Scholar
  13. Yu Chao, Wen Qingzhen, Yu Hongwei et al. (2010), “Comparision of Properties of Styrene-butadiene Rubber Aged in Sea Water and in Hot Air,” China Synihetc Rubber Industry, 33(01):56–59. (in Chinese)Google Scholar
  14. Amin AFMS, Alam MS and Okui Y (2002), “An Improved Hyperelasticity Relation in Modeling Viscoelasticity Response of Natural and High Damping Rubbers in Compression: Experiments, Parameter Identification and Numerical Verification,” Mechanics of Materials, 34: 75–95.CrossRefGoogle Scholar
  15. Amin AFMS, Wiraguna SI, Bhuiyan AR and Okui Y (2006), “Hyperelasticity Model for Finite Element Analysis of Natural and High Damping Rubbers in Compression and Shear,” Journal of Engineering Mechanics, 132: 54–64.CrossRefGoogle Scholar
  16. Xing CX, Wang H, Li AQ et al. (2012), “Design and Experimental Verification of a New Multi-functional Bridge Seismic Isolation Bearing,” Journal of Zhejiang University-Science A (Applied Physics and Engineering), 13(12): 904–914.CrossRefGoogle Scholar
  17. Wang RZ, Chen SK, Liu KY et al. (2014), “Analytical Simulations of the Steel-laminated Elastomeric Bridge bearing,” Journal of Mechanics, 30(4): 373–382.CrossRefGoogle Scholar
  18. Itoh Y, ASCE M and Gu HS (2009), “Prediction of Aging Characteristics in Natural Rubber Bearings Used in Bridges,” Journal of Bridge Engineering, 14(2): 122–128.CrossRefGoogle Scholar
  19. Gu HS and Itoh Y (2010), “Aging Behaviour of Natural Rubber and High Damping Rubber Materials Used in Bridge Rubber Bearings,” Advances in Structural Engineering, 13(6): 1105–1113.CrossRefGoogle Scholar
  20. Kim Dookie, Oh Ju and Do Jeongyun (2014), “Effects of Thermal Aging on Mechanical Properties of Laminated Lead and Natural Rubber Bearing,” Earthquakes and Structures, 6(2): 127–140.CrossRefGoogle Scholar
  21. Zhong Jianlin, Ren Jie and Ma Dawei (2015), “Constitutive Model and Its Application for Rubber Material based on Exp-in Model and Generalized Viscoelastic Theory,” Journal of Vibration and Shock, 34(19): 150–156. (in Chinese)Google Scholar
  22. Zuo Liang and Xiao Feixiong (2008), “One Method of Determination for Material Constants of Rubber Moony-rivlin Model,” Machine Building, 46(527): 38–40. (in Chinese)Google Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Guifeng Zhao
    • 1
    • 4
  • Yuhong Ma
    • 2
  • Yanmin Li
    • 1
  • Jiarun Luo
    • 3
  • Chang Du
    • 1
  1. 1.School of Civil EngineeringGuangzhou UniversityGuangzhouChina
  2. 2.Earthquake Engineering Research & Test Center, Key Laboratory of Seismic Control and Structural SafetyGuangzhou UniversityGuangzhouChina
  3. 3.Shanghai Construction Engineering Technology Co., Ltd.ShanghaiChina
  4. 4.School of Civil EngineeringGuangzhou UniversityGuangzhouChina

Personalised recommendations