On the constitutive modeling of reinforced rubber in a broad frequency domain

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 90, Issue 5, 2010, Pages 418-435

  Suwannachit, Anuwat ^a   Nackenhorst, Udo ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Complex modulus; Mullins effect; Pseudo elasticity; Rubber elasticity; Viscoelasticity

Indexed keywords

EID: 77951738347     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200900360     Document Type: Article

References (38)

1. M. Brinkmeier and U. Nackenhorst, An approach for large-scale gyroscopic eigenvalue problems with application to high-frequency response of rolling tires, Comput. Mech. 41, 503-515 (2008).
2. J.H. Cho and S.K. Youn, A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect, Arch. Appl. Mech. 75, 275-288 (2006).
3. A. Drozdov, A model for the nonlinear viscoelastic response in polymers at finite strains, Int. J. Solids Struct. 35, 2315-2347 (1998).
4. S. Govindjee and S. Reese, A presentation and comparison of two large deformation viscoelasticity models, Trans ASME J. Eng. Mater. Technol. 119, 251-255 (1997).
5. S. Govindjee and J. Simo, Mullins' effect and the strain amplitude dependence of the storage modulus, Int. J. Solids Struct. 29, 1737-1751 (1992).
6. Z. Guo and L.J. Sluys, Computational modelling of the stress-softening phenomenon of rubber-like materials under cyclic loading, Eur. J. Mech. A, Solids 25, 877-869 (2006).
7. P. Haupt and A. Lion, On finite linear viscoelasticity of incompressible isotropic materials, Acta Mech. 159, 87-124 (2002).
8. G. Heinrich and M. Kaliske, Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity, Comput. Theor. Polym. Sci. 7, 227-241 (1998).
9. P. Höfer and A. Lion, Modelling of frequency-and amplitude-dependent material properties of filler-reinforced rubber, J. Mech. Phys. Solids 57, 500-520 (2009).
10. G.A. Holzapfel, On large strain viscoelasticity: continuum formulation and finite element applications to elastomeric structures, Int. J. Numer. Methods Eng. 39, 3909-3926 (1996).
11. G.A. Holzapfel, Nonlinear solid mechanics: a continuum approach for engineering (Wiley, New York, 2000).
12. G. Holzapfel and J.C. Simo, A new viscoelastic constitutive model for continuous media at finite thermomechanical changes, Int J. Solids Struct. 33, 3019-3034 (1996).
13. M. Kaliske and G. Heinrich, An extended tube-model for rubber elasticity: statistical-mechanical theory and finite element implementation, Rubber Chem. Technol. 72, 602-632 (1999).
14. M. Kaliske, L. Nasdala, and H. Rothert, On damage modelling for elastic and viscoelastic materials at large strain, Comput. Struct. 79, 2133-2141 (2001).
15. M. Kaliske and H. Rothert, Formulation and implementation of three-dimensional viscoelasticity at small and finite strains, Comput. Mech. 19, 228-239 (1997).
16. B.K. Kim and S.K. Youn, A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation, Arch. Appl. Mech. 71, 748-763 (2001).
17. B.K. Kim, S.K. Youn, and W.S. Lee, A constitutive model and fea of rubber under small oscillatory load superimposed on large static deformation, Arch. Appl. Mech. 73, 781-798 (2004).
18. P. Le Tallec, C. Rahier, and A. Kaiss, Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation, Comp. Methods Appl. Mech. Eng. 109, 233-258 (1993).
19. A. Lion, A constitutive model for carbon black filled rubber: Experimental investigations and mathematical representation, Contin. Mech. Thermodyn. 8, 153-169 (1996).
20. A. Lion, On the large deformation behaviour of reinforced rubber at different temperatures, J. Mech. Phys. Solids 45, 1805-1834 (1997).
21. A. Lion, A physically based method to represent the thermo-mechanical behaviour of elastomers, Acta Mech. 123, 1-25 (1997).
22. A. Lion and C. Kardelky, The payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales, Int. J. Plast. 20, 1313-1345 (2004).
23. A. Lion, J. Retka, and M. Rendek, On the calculation of predeformation-dependent dynamic modulus tensors in finite nonlinear viscoelasticity, Mech. Res. Commun. 36, 653-658 (2009).
24. J. Lubliner, A model of rubber viscoelasticity, Mech. Res. Commun. 12, 93-99 (1985).
25. J. Mackerle, Rubber and rubber-like materials, finite-element analyses and simulations, an addendum: a bibliography (1997-2003), Model. Simul. Mater. Sci. Eng. 12, 1031-1053 (2004).
26. C. Miehe, Discontinuous and continuous damage evolution in ogden-type large-strain elastic materials, Eur. J. Mech. A, Solids 14,697-720 (1995).
27. K.N. Morman and J.C. Nagtegaal, Finite element analysis of sinusoidal small-amplitude vibrations in deformed viscoelastic solids. part 1: Theoretical development, Int. J. Numer. Methods Eng. 19, 1079-1103 (1983).
28. L. Mullins, Effect of stretching on the properties of rubber, J. Rubber Res. 16, 257-289 (1947).
29. L. Nasdala, Ein viskoelastisches Schädigungsgesetz für den stationär rollenden Reifen, PhD thesis (Leibniz Universität Hannover, Hannover, 2000).
30. R.W. Ogden and D.G. Roxburgh, A pseudo-elastic model for the mullins effect in filled rubber, Proc. R. Soc. Lond. A 455, 459-490 (1999).
31. S. Reese and S. Govindjee, Theoretical and numerical aspects in the thermo-viscoelastic material behaviour of rubber-like polymers, Mech. Time-Depend. Mater. 1, 357-396 (1998).
32. S. Reese and S. Govindjee, A theory of finite viscoelasticity and numerical aspects, Int. J. Solids Struct. 35, 3455-3482 (1998).
33. F. Sidoroff, Un modèle viscoélastique non linéaire avec configuration intermédiaire, J. Mec. 13, 679-713 (1974).
34. J.C. Simo, On a fully three-dimensional finite-strain viscoelastic damage model, Comp. Methods Appl. Mech. Eng. 60, 153-173 (1987).
35. J.C. Simo and T.J.R. Hughes, Computational Inelasticity (Springer, Berlin, Heidelberg, New York, 1998).
36. P. Wriggers, Nonlinear finite element methods (Springer, Berlin, Heidelberg, New York, 2008).
37. M. Ziefle, Numerische Konzepte zur Behandlung inelastischer Effekte beim reibungsbehafteten Rollkontakt, PhD thesis (Leibniz Universität Hannover, Hannover, 2007).
38. M. Ziefle and U. Nackenhorst, Numerical techniques for rolling rubber wheels: treatment of inelastic materials properties and frictional contact, Comput. Mech. 42, 337-356 (2008).