Prediction of Strain Energy Function for Butyl Rubbers

부틸고무의 변형률 에너지 함수 예측

  • 김남웅 (서울대학교 대학원 기계항공공학부) ;
  • 김국원 (순천향대학교 기계공학과)
  • Published : 2006.10.01


Up to now, several mathematical theories based on strain energy functions have been developed for rubber materials. These theories, coupled with the finite element method, can be used very effectively by engineers to analyze and design rubber components. However, due to the complexities of the mathematical formulations and the lack of general guidelines available fur the analysis of rubber components, it is a formidable task for an engineer to analyze rubber components. In this paper a method for predicting strain energy functions - Neo-Hookean model and Mooney-Rivlin model - from the hardness using the empirical equation without any experiment is discussed. First based on the elasticity theories of rubber, the relation between stress and strain is defined. Then for the butyl rubbers, the model constants of Neo-Hookean model and Mooney-Rivlin model are calculated from uniaxial tension tests. From the results, the usefulness of the empirical equation to estimate elastic modulus from hardness is confirmed and, fur Mooney-Rivlin model, the predicted and the experimental model constants are compared and discussed.


Butyl Rubber;Hardness;Strain Energy Function;Mooney-Rivlin Model;Neo-Hookean Model


  1. James, A. G., Green, A. and Simpson, G. M., 1975, 'Strain Energy Functions of Rubber 1. Characterization of Gum Vulcanizates,' Journal of Applied Polymer Science, Vol. 19, pp. 2033-2058
  2. Haines, D. W. and Wilson, W. D., 1979, 'Strain Energy Density Function for Rubberlike Materials,' Journal of the Mechanics and Physics of Solids, Vol. 27, pp. 345-360
  3. Kim, W. D., ·Kim, W. S., Kim, D. J., Woo, C. S. and Lee, H. J., 2004, 'Mechanical Testing and Nonlinear Material Properties for Finite Element Analysis of Rubber Components,' Trans. of the KSME(A), Vol. 28, No.6, pp. 848-859
  4. Treloar, L. R. G., 1975, The Physics of Rubber Elasticity, 3d Ed., Clarendon, Oxford
  5. Finney, R. H. and Kumar, A., 1988, 'Development of Material Constants for Nonliner Finite Element Analysis,' Rubber Chemistry and Technology, Vol. 61, pp. 879-891
  6. Yeoh, O. H., 1984, 'On Hardness and Youngs Modulus of Rubber,' Plastics and Rubber Processing and Appl., Vol. 4, No.2, pp. 141-144
  7. Gent, A. N., 1958, 'On the Relation Between Indentation Hardness and Young's Modulus,' Rubber Chemistry and Technology, Vol. 31, pp . 896-906

Cited by

  1. Sensitivity Control and Design of the Silicone Foot Sensor Using FEM vol.31, pp.11, 2014,
  2. Investigation of a Novel Rubber-Forming Process Inducing Uniform Surface Pressure for the Fabrication of a Thin Bent Plate with Corrugated Structure vol.35, pp.8, 2011,