Sage Journals: Discover world-class research

Abstract

The equilibrium stress-stretch behavior of elastomeric materials can be captured by statistical mechanics treatments of rubber elasticity. Gaussian statistics is known to capture the essence of the stress-strain behavior; however, discrepancies between Gaussian theory and experiment are recognized to occur at both small to moderate stretch levels and at large stretch levels. These discrepancies are further amplified in studies of the effects of swelling on stress-stretch behavior. A brief review of the various approaches used to represent the stress-stretch behavior of elastomers and the effect of swelling on this behavior is given. Then, hybrid constitutive model composed of the Flory-Erman constrained chain model and the Arruda-Boyce non-Gaussian eight-chain model is presented and found to capture the stress-stretch behavior from small to large stretch levels. Furthermore, the Flory-Erman/Arruda-Boyce hybrid model is also found to successfully predict the effect of swelling on the stress-stretch behavior from small to large stretches using only three material constants.

Keywords

elastomers swelling constitutive models stress-strain behavior

Get full access to this article

View all access options for this article.

References

[1] Treloar, L.R.G. : The Physics of Rubber Elasticity, Oxford University Press, Oxford, 1975.

[2] Boyce, M. C. and Arruda, E. M. : Constitutive models of rubber elasticity: A review. Rubb. Chem. Techn., 73, 504-523 (2000).

[3] Arruda, E. M. and 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).

[4] Flory, P J. and Erman, B. : Theory of elasticity of polymer networks. Macromolecules, 15, 800-806 (1982).

[5] Wall, F T. and Flory, P S. : Statistical thermodynamics of rubber elasticity. J. Chem. Phys., 19, 1435-1435 (1951).

[6] Flory, P J. : Thermodynamic relations for high elastic materials. Trans. Faraday Soc., 57, 829-829 (1961).

[7] Bischoff, J. E. , Arruda, E. M. , and Grosh, K. : A new constitutive model for the compressibility of elastomers at finite deformations. Rubb. Chem. Techn., (in press).

[8] Allen, G. , Kirkham, M. J. , Padget, J. , and Price, C. : Thermodynamics of rubber elasticity at constant volume. Trans. Faraday Society, 67, 1278-1292 (1971).

[9] Gumbrell, S. M. , Mullins, L. J. , and Rivlin, R. S. : Departures of the elastic behavior of rubber in simple extension from the kinetic theory. Trans. Faraday Society, 49, 1495-1505 (1953).

10.

[10] Erman, B. and Flory, P J. : Relationships between stress, strain, and molecular constitution of polymer networks: Comparison of theory with experiments. Macromolecules, 15, 806-811 (1982).

11.

[11] Flory, P J. and Tatara, Y-I. : The elastic free energy and elastic equation of state: Elongation and swelling of PDMS networks. J. Polymer Science, Polymer Physics Edition, 13, 683-702 (1975).

12.

[12] Rivlin, R. S. and Saunders, D. W. : Large elastic deformations of isotropic materials VII: Experiments on the deformation of rubbers. Phil. Trans. Roy. Soc., London, A243, 251-288 (1951).

13.

[13] Erman, B. and Flory, P J. : Rubber elasticity in the range of small uniaxial tensions and compressions: Results for polydimethylsiloxane. J. Polymer Science: Polymer Physics Edition, 16, 1115-1121 (1978).

14.

[14] McKenna, G. B. , Flynn, K. M. , and Chen, Y. : Experiments on the elasticity of dry and swollen networks: Implications of the Frankel-Flory-Rehner hypothesis. Macromolecules, 22, 4507-4512 (1989).

15.

[15] Mullins, L. : Determination of degree of crosslinking in natural rubber vulcanizates: Part IV Stress-strain behavior at large extensions. J. Appl. Polymer Science, (11-6), 257-263 (1959).

16.

[16] Flory, P J. : Theory of elasticity of polymer networks: The effects of local constraints on junctions. J. Chem. Phys., 66, 5720-5720 (1977).

17.

[17] Wu, P D. and van der Giessen, E. : On improved network models of rubber elasticity and their applications to oriented glassy polymers. J. Mech. Phys. Solids, 41, 427-427 (1993).

18.

[18] Flory, P J. : The elastic free energy of dilation of a network. Macromolecules, 12, 119-122 (1979).

19.

[19] Erman, B. and Flory, P J. : Theory of elasticity of polymer networks II: The effect of geometric constraints on junctions. J. Chem. Phys., 68 (12), 5363-5369 (1978).

20.

[20] Wagner, M. H. : The origin of the C2 term in rubber elasticity. J Rheol., 38, 655-679 (1994).

21.

[21] Han, N. H. , Horkay, F. , and McKenna, G. B. : Mechanical and swelling behavior of rubber: A comparison of some molecular models with experiment. Math. Mech. Solids, 4, 139-167 (1999).

Swelling and Mechanical Stretching of Elastomeric Materials

Abstract

Keywords

Get full access to this article

References