A theoretical model is proposed to describe the damaged hyperelastic behavior of filled rubber-like solids. Special emphasis is laid on two specific phenomena: the Mullins effect (i.e., strain induced stress softening) and irreversible (i.e., permanent) strain. Often observed in the behavior of the hyperelastic rubber-like materials, these two phenomena are supposed to be exclusively induced (and then governed) by isotropic damage (cavities and holes) initiation and growth. Using the classical Continuum Damage Mechanics (CDM) together with the generalized normality rule, a constitutive model is proposed to account for these two effects of damage. After a choice of constitutive functions, the obtained model is applied to four different loading paths classically studied in the case of this type of filled elastomeric material.
Get full access to this article
View all access options for this article.
References
1.
1. Andreux, F., Saanouni, K. 1994. "Moddlisation du comportement hyper-viscoélastique à variation de volume induite par l'endommagement," in Colloque international de mécanique de caoutchoucs et des polymères, G'sellet al. (editors), Nancy,25-26, Octobre 1994.
2.
2. Andrieux, F. 1996. "Sur les milieux visco-hyperélastiques endommageables," Thèse de doctorat, D895, Univ. de Technologie de Compiègne.
3.
3. Andrieux, F., Saanouni, K., Sidoroff, F.1997. "Sur les solides hyperélastiques à variation de volume induite par l'endommagement,"C.R.A.S., série II, tome 324, no. 5, Paris: 281-288.
4.
4. Andrieux, F., Saanouni, K.1997. "A finite strain hyperelastic model for the quasi-static behaviour of rubber-like materials," Submitted to Continuum Mechanics and Thermodynamics.
5.
5. Chaboche, J. L. 1977. "Sur l'utilisation des variables d'état internes pour la description du comportement viscoplastique et de la rupture par l'endommagement,"Symp. Franco-Polonais de Rhéologie et Mécanique, Cracovie, Poland.
6.
6. Chaboche, J. L. 1978. "Description thermodynamique et phénoménologique de la viscoplasticité cyclique avec endommagement," Thèse d'état, Univ. Paris VI.
7.
7. Dragon, A., Fanget, A., Trumel, H.1996. "A coupled viscoelastic-viscoplastic finite strain model for a rubber-like particular composite,"IUTAM Symposium on Micromechanics of plasticity and damage multiphase materials, Kluwer Academic Publishers: 191-198.
8.
8. Govindjee, S., Simo, R.1991. "A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins' effect,". J. Mech. Phy. Sol., 39:87-112.
9.
9. Green, A. E., Adkins, J. E.1970. Large elastic deformations, Clarendon Press, Oxford.
10.
10. Heuillet, P. 1992. "Caractérisation de l'endommagement des propergols solides composites," Thèse de doctrat, Univ. de Technolegie de Compiègne.
11.
11. Heuillet, P., Roumagnac, P., Dugoutier, L.1995. "Modélisation du comportement hyperélastique des élastomères,"Mécamat Infos, 15.
12.
12. Lee, E. H. 196. "Elastic-plastic deformation at finite strains,"J. App. Mech., 36:1-6.
13.
13. Lepie, A. H., Adicoff, A.1975. "Energy balances and uniaxial damage of highly filled elastomers,"J. App. Polymer Science, Vol. 19, pp: 2821-2830.
14.
14. Lion, A.1996. "A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation,"Cont. Mech. Thermodyn., Vol. 8, pp: 153-169.
15.
15. Mullins, L., Tobin, R. N.1965. "Stress softening in rubber vulcanizates,"J. Appl. Pol. Sci., 9:2993-3009.
16.
16. Odgen, R. W.1984. Non-linear elastic deformations, Ellis Horwood, London.
17.
17. Pilvin, P., Cailletaud, G."Identification and inverse problems related to material behavior,"Proc. Sec. Int. Symp. on Inverse Problems, Paris2-4 November 1994, pp: 79-86, Buiet al Editors.
18.
18. Saanouni K., Sidoroff F., Andrieux, F.1998. "Damage hyperelastic solid with induced volume variation. Effect of loading paths," in Damage Mechanics in Engineering Materials, Edited by G. Z. Voyiadjis, J. W. Ju and J. L. Chaboche, Elsevier, pp. 503-522.
19.
19. Sidoroff, F.1973. "The geometrical concept of intermediate configuration and elastic-plastic finite strain,"Arch. Mech., 25:299-309.
20.
20. Sidoroff, F.1975. "Variables internes en viscoélasticité: II Milieux avec configuration intermédiaire,"J. de Méc., 13:679-713.
21.
21. Trumel, H., Fanget, A., Dragon, A.1996. "A finite strain elastic-plastic model for the quasi-static behaviour of particulate composites,"Int. J. Engng. Sci., Vol. 34, No. 6, pp. 677-698.
22.
22. Mooney, M.1940. "A theory of large elastic deformation,"Journal of Applied Physics, Vol. 11, p. 582.
