Determination of Strain Energy Function of Rubber Materials Considering Stress Softening Behavior

응력연화거동을 고려한 고무 재료의 변형률 에너지 함수 결정

  • Kim, W.S. (Department of Mechanical Engineering, Chungnam National University Graduation School) ;
  • Hong, S.I. (Department of Mechanical Engineering, Chungnam National University)
  • 김완수 (충남대학교 기계공학과 대학원) ;
  • 홍성인 (충남대학교 기계공학과)
  • Published : 2007.09.29


When the rubber vulcanizates reinforced with carbon black or silica are subjected to cyclic loading from its virgin state, the stress required on reloading is less than that on the initial loading. This stress softening phenomenon is referred to as the Mullins effect. The strain energy function of rubber vulcanizates was investigated using theory of pseudo-elasticity incorporated damage parameter that Ogden and Roxburgh have proposed to describe the damage-induced stress softening effect in rubber-like solids. The quasi-static cyclic loading test was performed using the NR-SBR vulcanizates reinforced with carbon black, and then the effect of a damage parameter to stress-strain curve in reloading and subsequent reloading paths was studied. The strain energy function of the rubber vulcanizates with a different filler content was also evaluated.


  1. W.D. Kim, C.S. Woo, K.S. Kim, and J.D. Kwon, 'An experimental study on the dynamic characteristics of rubber isolator', Elastomer, 37, 183 (2002)
  2. L. Mullins, 'Softening of rubber by deformation', Rubber Chem. Tech., 42, 339 (1969)
  3. M.A. Johnson and M.F. Beatty, 'The Mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string', Continuum Mech. Thermodyn. 5, 83 (1993)
  4. C. Miehe, 'Discontinuous and continuous damage evloution in Ogden type large strain elastic materials', Eur. J. Mech. A Solids, 14, 69 (1995)
  5. G. Chagnon, E. Verron, L. Gornet, G. Marckmann, and P. Charrier, 'On the relevance of continuum damdage mechanics as applied to the Mullins effect in elastomers', J. Mech. Phys. Soilds, 52, 1627 (2004)
  6. R.W. Ogden and D.G. Roxburgh, 'A pseudo-elastic model for the Mullins effect in filled rubber', Proc. R. Soc. Lond., 455, 2861 (1999)
  7. E.M. Arruda and M.C. Boyce, 'A three dimensional constitutive model for the large stretch behavior of rubber elastic materials', J. Mech. Phys. Solids, 41, 389 (1993)
  8. M. Mooney, 'A theory of large elastic deformation', J. Appl. Phys., 11, 582 (1940)
  9. R. Ogden, 'Recent advances in the phenomenological theory of rubber elasticity', Rubber Chem. Tech., 59, 361 (1984)
  10. W.D. Kim, W.S. Kim, D.J. Kim, C.S. Woo, and H.J. Lee, 'Mechanical testing and nonlinear material properties for finite element analysis of rubber components', Trans. of the KSME, 28, 848 (2004)
  11. S. Govindjee and J. Simo, 'A micromechanically based continuum damage model for carbon blackfilled rubber incoporating Mullins' effect', J. Mech. Phys. Solids, 39, 87 (1991)