Constitutive equations for the nonlinear elastic response of rubbers

Acta Mechanica

Volumn 185, Issue 1-2, 2006, Pages 31-65

  Drozdov, A D ^a   Christiansen, J DeClaville ^a  

^a Aalborg University ^*  (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITION; COMPUTATIONAL GEOMETRY; CONSTRAINT THEORY; ELASTOMERS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS;

CONSTITUTIVE EQUATIONS; FLORY-ERMAN AND ERMAN-MONNERIE APPROACHES; NONLINEAR ELASTIC RESPONSE;

RUBBER;

EID: 33746075174     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-006-0342-7     Document Type: Article

References (50)

1. Treloar, L. R. G.: The physics of rubber elasticity. Oxford: Clarendon Press 1975.
2. Erman, B., Mark, J. E.: Structures and properties of rubberlike networks. Oxford: Oxford University Press 1998.
3. Yeoh, O. H., Fleming, P. D.: A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity. J. Polym. Sci. Part B: Polym. Phys. 35, 1919-1931 (1997).
4. Han, W. H., Horkay, F., McKenna, G. B.: A comparison of some rubber network models with stress-strain data on dry and swollen polymer rubbers. Math. Mech. Solids 4, 139-167 (1999).
5. Boyce, M. C., Arruda, E. M.: Constitutive models of rubber elasticity: a review. Rubber Chem. Technol. 73, 504-523 (2000).
6. Kloczkowski, A.: Application of statistical mechanics to the analysis of various physical properties of elastomeric networks - a review. Polymer 43, 1503-1525 (2002).
7. Rubinstein, M., Panyukov, S.: Elasticity of polymer networks. Macromolecules 35, 6670-6686 (2002).
8. Heinrich, G., Kaliske, M., Kluppel, M., Mark, J. E., Staube, E., Vilgis, T. A.: The thermoelasticity of rubber-like materials and related constitutive laws. J. Macromol. Sci. Part A: Pure Appl. Chem. 40, 87-93 (2003).
9. Kawamura, T., Urayama, K., Kohjiya, S.: Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 5. Revisit to Mooney-Rivlin approach to strain energy density function. J. Soc. Rheol. Japan 31, 213-217 (2003).
10. Gottlieb, M., Gaylord, R. J.: Experimental tests of entanglement models of rubber elasticity. 3. Biaxial deformations. Macromolecules 20, 130-138 (1987).
11. Meissner, B., Matejka, L.: Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis. Polymer 43, 3803-3809 (2002).
12. Meissner, B., Matejka, L.: A Langevin-elasticity-theory-based constitutive equation for rubber-like networks and its comparison with biaxial stress-strain data. Part I. Polymer 44, 4599-4610 (2003).
13. Meissner, B., Matejka, L.: A Langevin-elasticity-theory-based constitutive equation for rubber-like networks and its comparison with biaxial stress-strain data. Part II. Polymer 45, 7247-7260 (2004).
14. Arruda, E. M., Boyce, M. C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41, 389-412 (1993).
15. Ball, R. C., Doi, M., Edwards, S. F., Warner, M.: Elasticity of entangled networks. Polymer 22, 1010-1018 (1981).
16. Edwards, S. F., Vilgis, T. A.: The tube model theory of rubber elasticity. Rep. Prog. Phys. 51, 243-297 (1988).
17. x) term. Polymer 35, 1819-1826 (1994).
18. Ronca, G., Allegra, G.: An approach to rubber elasticity with internal constraints. J. Chem. Phys. 63, 4990-4997 (1975).
19. Flory, P. J.: Theory of elasticity of polymer networks. The effect of local constraints on junctions. J. Chem. Phys. 66, 5720-5729 (1977).
20. Erman, B., Flory, P. J.: Theory of elasticity of polymer networks. II. The effect of geometric constraints on junctions. J. Chem. Phys. 68, 5363-5369 (1978).
21. Flory, P. J., Erman, B.: Theory of elasticity of polymer networks. 3. Macromolecules 15, 800-806 (1982).
22. Erman, B., Monnerie, L.: Theory of elasticity of amorphous networks: effect of constraints along chains. Macromolecules 22, 3342-3348 (1989).
23. Kloczkowski, A., Mark, J. E., Erman, B.: A diffused-constraint theory for the elasticity of amorphous polymer networks. 1. Fundamentals and stress-strain isotherms in elongation. Macromolecules 28, 5089-5096 (1995).
24. Kloczkowski, A., Mark, J. E., Erman, B.: A diffused-constraint theory for the elasticity of amorphous polymer networks. 2. Molecular deformation tensors and strain birefringence. Comput. Theor. Polym. Sci. 5, 37-45 (1995).
25. Everaers, R.: Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model. Eur. Phys. J. B 4, 341-350 (1998).
26. Kachanov, L. M.: Introduction to continuum damage mechanics. Dordrecht: Martinus-Nijhoff 1986.
27. Lemaitre, J.: A Course of damage mechanics. Berlin: Springer 1992.
28. Ogden, R. W., Roxburgh, D. G.: A pseudo-elastic model for the Mullins effect in filled rubber. Proc. Roy. Soc. London A 455, 2861-2878 (1999).
29. Criscione, J. C.: Rivlin's representation formula is ill-conceived for the determination of response functions via biaxial testing. J. Elasticity 70, 129-147 (2003).
30. Edwards, S. F.: The statistical mechanics of polymers with excluded volume. Proc. Phys. Soc. (London) 85, 613-624 (1965).
31. Doi, M., Edwards, S. F.: The theory of polymer dynamics. Oxford: Clarendon Press 1986.
32. Kleinert, H.: Path integrals in quantum mechanics, statistics, and polymer physics. Singapore: World Scientific 1995.
33. Heinrich, G., Kaliske, M.: Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity. Comput. Theor. Polym. Sci. 7, 227-241 (1997).
34. Kaliske, M., Heinrich, G.: An extended tube-model for rubber elasticity: statistical-mechanical theory and finite element implementation. Rubber Chem. Technol. 72, 602-632 (1999).
35. Kutter, S., Terentjev, E. M.: Tube model for the elasticity of entangled nematic rubbers. Eur. Phys. J. E 6, 221-229 (2001).
36. Drozdov, A. D.: Finite elasticity and viscoelasticity. Singapore: World Scientific 1996.
37. Drozdov, A. D., Gottlieb, M.: Ogden-type constitutive equations in finite elasticity of elastomers. Acta Mech. in press (2006).
38. Marrucci, G.: Rubber elasticity theory. A network of entangled chains. Macromolecules 14, 434-442 (1981).
39. Fukahori, Y., Seki, W.: Molecular behaviour of elastomeric materials under large deformation: 1. Re-evaluation of the Mooney-Rivlin plot. Polymer 33, 502-508 (1992).
40. 2 term in rubber elasticity. J. Rheol. 38, 655-679 (1994).
41. Elias-Zuniga, A., Beatty, M. F.: Constitutive equations for amended non-Gaussian network models of rubber elasticity. Int. J. Engng. Sci. 40, 2265-2294 (2002).
42. Attard, M. M., Hunt, G. W.: Hyperelastic constitutive modeling under finite strain. Int. J. Solids Struct. 41, 5327-5350 (2004).
43. Miroshnychenko, D., Green, W. A., Turner, D. M.: Composite and filament models for the mechanical behaviour of elastomeric materials. J. Mech. Phys. Solids 53, 748-770 (2005).
44. James, A. G., Green, A., Simpson, G. M.: Strain energy functions of rubber. I. Characterization of gum vulcanizates. J. Appl. Polym. Sci. 19, 2033-2258 (1975).
45. Kawabata, S., Matsuda, M., Tei, K., Kawai, H.: Experimental survey of the strain energy density function of isoprene rubber vulcanizate. Macromolecules 14, 154-162 (1981).
46. Glucklich, J., Landel, R. F.: Strain energy function of styrene butadiene rubber and the effect of temperature. J. Polym. Sci.: Polym. Phys. Ed. 15, 2185-2199 (1977).
47. Urayama, K., Kawamura, T., Kohjiya, S.: Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 4. Further assessment of the slip-link model for chain-entanglement effect on rubber elasticity. J. Chem. Phys. 118, 5658-5664 (2003).
48. Jones, D. F., Treloar, L. R. G.: The properties of rubber in pure homogeneous strain. J. Phys. D: Appl. Phys. 8, 1285-1304 (1975).
49. Ogden, R. W.: Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proc. Roy. Soc. London A 326, 565-584 (1972).
50. Vangerko, H., Treloar, L. R. G.: The inflation and extension of rubber tube for biaxial strain studies. J. Phys. D: Appl. Phys. 11, 1969-1978 (1978).