Interaction and multiscale mechanics

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Computational modelling for description of rubber-like materials with permanent deformation under cyclic loading

  • Guo, Z.Q. (Faculty of Civil Engineering and Geosciences, Delft University of Technology) ;
  • Sluys, L.J. (Faculty of Civil Engineering and Geosciences, Delft University of Technology)
  • Received : 2008.01.30
  • Accepted : 2008.07.08
  • Published : 2008.09.25
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Abstract

When carbon-filled rubber specimens are subjected to cyclic loading, they do not return to their initial state after loading and subsequent unloading, but exhibit a residual strain or permanent deformation. We propose a specific form of the pseudo-elastic energy function to represent cyclic loading for incompressible, isotropic materials with stress softening and residual strain. The essence of the pseudo-elasticity theory is that material behaviour in the primary loading path is described by a common elastic strain energy function, and in unloading, reloading or secondary unloading paths by a different strain energy function. The switch between strain energy functions is controlled by the incorporation of a damage variable into the strain energy function. An extra term is added to describe the permanent deformation. The finite element implementation of the proposed model is presented in this paper. All parameters in the proposed model and elastic law can be easily estimated based on experimental data. The numerical analyses show that the results are in good agreement with experimental data.

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References

  1. Beatty, M.F. and Krishnaswamy, S.A. (2000), "Theory of stress softening in incompressible isotropic elastic materials", J. Mech. Physics. Solids., 48, 1931-1965. https://doi.org/10.1016/S0022-5096(99)00085-X
  2. Besdo, D. and Ihlemann, J. (2003), "A phonological constitutive model for rubberlike materials and its numerical applications", Int. J. Plasticity., 19, 1019-1036. https://doi.org/10.1016/S0749-6419(02)00091-8
  3. Dorfmann, A. and Ogden, R.W. (2004), "A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber", Int. J. Solids. Struct., 41, 1855-1878. https://doi.org/10.1016/j.ijsolstr.2003.11.014
  4. Dorfmann, A. and Ogden, R.W. (2003), "A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubber", Int. J. Solids. Struct., 40, 2699-2714. https://doi.org/10.1016/S0020-7683(03)00089-1
  5. Drozdov, A.D. and Dorfmann, A. (2001), "Stress-strain relations in finite viscoelastoplasticity of rigid-rod networks: applications to the Mullins effect", Continuum Mech. Thermodyn., 13, 183-205. https://doi.org/10.1007/s001610100049
  6. Gao, Y.C. (1997), "Large deformation field near a crack tip in a rubber-like material", Theoretical Appl. Fract. Mech., 26, 155-162. https://doi.org/10.1016/S0167-8442(96)00044-4
  7. Govindjee, S. and Simó, J.C. (1992a), "Transition from micro-mechanics to computationally efficient phenomenology: carbon black filled rubbers incorporating Mullins' effect", J. Mech. Physics Solids, 40, 213-233. https://doi.org/10.1016/0022-5096(92)90324-U
  8. Govindjee, S. and Simo, J.C. (1992b), "Mullins' effect and the strain amplitude dependence of the storage modulus", Int. J. Solids Struct., 29, 1737-1751. https://doi.org/10.1016/0020-7683(92)90167-R
  9. Guo, Z.Q. (2006), "Computrational modeling of rubber-like materials under monotonic and cyclic loading", PhD thesis, Delft University of Technology.
  10. Guo, Z.Q. and Sluys, L.J. (2006a), "Computational modelling of the stress-softening phenomenon of rubber-like materials under cyclic loading", European J. Mech., A/Solids, 25, 877-896. https://doi.org/10.1016/j.euromechsol.2006.05.011
  11. Guo, Z.Q. and Sluys, L.J. (2006b), "Application of constitutive models for description of rubber-like materials under monotonic loading", Int. J. Solids Struct., 43, 2799-2819. https://doi.org/10.1016/j.ijsolstr.2005.06.026
  12. Harwood, J.A.C., Mullins, L. and Payne, A.R. (1967), "Stress softening in rubbers - A review", J. Institution of the Rubber Industry, 1, 17-27.
  13. Krishnaswamy, S.A. and Beatty, M.F. (2000), "The Mullins effect in compressible solids", Int. J. Eng. Sci., 38, 1397-1414. https://doi.org/10.1016/S0020-7225(99)00125-1
  14. Lion, A. (1996) "A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation", Continuum Mech. Thermodyn., 8, 153-169. https://doi.org/10.1007/BF01181853
  15. Lion, A. (1997), "On the large deformation behaviour of reinforced rubber at different temperatures", J. Mech. Physics. Solids., 45, 1805-1834. https://doi.org/10.1016/S0022-5096(97)00028-8
  16. Miehe, C. and Keck, J (2000), "Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation", J. Mech. Physics. Solids., 48, 323-365. https://doi.org/10.1016/S0022-5096(99)00017-4
  17. Mullins, L. (1947), "Effect of stretching on the properties of rubber", J. Rubber Res., 16, 275-289.
  18. Mullins, L. and Tobin, N.R. (1957), "Theoretical model for the elastic behaviour of filler-reinforced vulcanized rubbers", Rubber Chemistry Technology, 30, 555-571. https://doi.org/10.5254/1.3542705
  19. Ogden, R.W. and Roxburgh, D.G. (1999), "A pseudo-elastic model for the Mullins effect in filled rubber", Proceedings of the Royal Society of London A, 2861-2877.
  20. Septanika, E.G. (1998), "A time-dependent constitutive model for filled and vulcanised rubbers", PhD thesis, Delft University of Technology.
  21. Zhong, A. (2005), "Discussion 'A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber, by A. Dorfmann and R.W. Ogden", Int. J. Solids Struct., 42, 3967-3969. https://doi.org/10.1016/j.ijsolstr.2004.12.002

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