Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity

Computational and Theoretical Polymer Science

Volumn 7, Issue 3-4, 1997, Pages 227-241

  Heinrich, G ^a   Kaliske, M ^b  

^a Materials Research ^*  (Germany)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Finite element application; Numerical modelling; Rubber elasticity; Statistical thermodynamics; Tube model

Indexed keywords

EID: 0001072935     PISSN: 10893156     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1089-3156(98)00010-5     Document Type: Article

References (72)

1. Treloar, L. R. G., The Physics of Rubber Elasticity. Clarendon Press, Oxford, 1975.
2. Flory, P. J., Principles of Polymer Chemistry. Cornell University, Ithaca, New York, 1953.
3. Dusek, K. and Prins, W., Adv. Polym. Sci., 1969, 6, 1.
4. Staverman, A. J., Adv. Polym. Sci., 1982, 44, 73.
5. Queslel, J. P. and Mark, J. E., Adv. Polym. Sci., 1984, 65, 135.
6. Heinrich, G., Sträube, E. and Helmis, G., Adv. Polym. Sci., 1988, 85, 33.
7. Edwards, S. F. and Vilgis, T. A., Rep. Prag. Phys., 1988, 51, 243.
8. Vilgis, T. A., in Comprehensive Polymer Science, Vol. 6, ed. G. Allen. Pergamon Press, 1989.
9. Eichinger, B. E., Ann. Rev. Phys. Chem., 1983, 34, 359.
10. Ullman, R., in Material Science and Technology, Vol. 12, eds R. W. Cahn, P. Haasen and E. J. Kramer. VCH, Weinheim, 1993.
11. Smith, Jr, K. J., in Comprehensive Polymer Science, 2nd supplement, ed. G. Allen. Pergamon Press, 1996.
12. Mark, J. E. and Erman, B. (eds), Elastomeric Polymer Networks. Prentice Hall, Englewood Cliffs, NJ, 1992.
13. Guth, E. and James, H. M., Ind. Eng. Chem., 1941, 33, 624.
14. James, H. M. and Guth, E., Ind. Eng. Chem., 1943, 35, 455.
15. Wall, F. T., J. Chem. Phys., 1943, 11, 527.
16. Treloar, L. R. G., Trans. Faraday Soc., 1943, 39, 241.
17. Flory, P. J. and Rehner, J. Jr, J. Chem. Phys., 1943, 11, 512.
18. Ronca, G. and Allegra, G., J. Chem. Phys., 1975, 63, 4990.
19. Flory, P. J., J. Chem. Phys., 1977, 66, 5720.
20. Erman, B. and Flory, P. J., J. Chem. Phys., 1978, 68, 5363.
21. Kastner, S., Faserforschung u. Textiltechnik/Z. Polymerforschunc, 1976,27,1.
22. Kastner, S., Acta Polymerica, 1980, 31, 444.
23. Kastner, S., Colloid Polym. Sci. 1981, 259, 499, 508.
24. Erman, B. and Monnerie, L., Macromolemles, 1982, 15, 800.
25. Marrucci, G., Macromolemles, 1981, 14, 434.
26. Gaylord, R., J. Polym. Eng. Sci., 1979,19, 263.
27. Gaylord, R., J. Polym. Bull., 1982, 8, 325.
28. Ball, R. C., Doi, M., Edwards, S. F. and Warner, M., Polymer, 1981,22,1010.
29. Deam, R. T. and Edwards, S. F., Phil. Trans. R. Soc. London, 1976, A280, 317.
30. Edwards, S. F. and Vilgis, T. A., Polymer, 1986, 27, 483.
31. Heinrich, G. and Sträube, E., Acta Polymerica, 1984, 35, 115.
32. Heinrich, G. and Sträube, E., Polym. Bull., 1987,17, 247.
33. Sträube, E., Urban, V., Pyckhout-Hintzen, W. and Richter, D., Macromolecules, 1994, 27, 7681.
34. Sträube, E., Urban, V., Pyckhout-Hintzen, W., Richter, D. and Glinka, C., W. Phys. Rev. Letters, 1995, 74, 4464.
35. Gronski, W. W., Hoffmann, W., Simon, G., Wutzier, A. and Sträube, E., Rubb. Chem. Technol., 1992, 65, 63.
36. Matzen, D. and Sträube, E., Colloid Polym. Sci., 1992, 270, 1.
37. Sträube, E. and Heinrich, G., Kautschuk Gummi. Kunststoffe, 1991,44,734.
38. Kluppel, M., Progr. Colloid Polym. Sci., 1992, 90, 137.
39. Kluppel, M. J., Appl. Polym. Sci., 1993, 48, 1137.
40. Kluppel, M. and Heinrich, G., Macromolecules, 1994, 27, 3569.
41. Kremer, K. and Grest, G. S., in MC and MD Simulations in Polymer Science, ed. K. Binder. Oxford University Press, 1994.
42. Edwards, S. F., Proc. Phys. Soc., 1965, 85, 613.
43. Edwards, S. F., in Polymer Networks, eds A. J. Chompff and S. Newman. Plenum Press, New York, 1989.
44. Heinrich, G. and Sträube, E., Makromol. Chem., Macromol. Symp., 1989, 30, 223.
45. Doi, M. and Edwards, S. F., J. Chem. Soc., Faraday Trans. 2, 1978,74, 1789, 1802, 1818.
46. Rubinstein, M. and Panyukov, S., Macromolecules, 1997, 30, 8036.
47. Read, D. J. and McLeish, T. C. B., Phys. Rev. Leiters, 1997,79,87.
48. Graessley, W. W. and Edwards, S. F., Polymer, 1981, 22, 1329.
49. Richter, D., Farago, B., Butera, R., Fetters, L. J., Huang, J. and Ewen, B., Macromolecules, 1993, 26, 795.
50. Blatz, P. J., Sharda, S. C. and Tschoegl, N. W., Trans. Soc. Rheot., 1974, 18, 145.
51. Ogden, R. W., Rubb. Chem. Techno!., 1973, 46, 398.
52. Chang, W. V., Bloch, R. and Tschoegl, N. W., in Chemistry and Properties of Crosslinked Polymers, ed. S. S. Labana. Academic Press, New York, 1977.
53. Flory, P. J., Proc. R. Soc. London, 1976, A 351, 351.
54. Graessley, W. W., Adv. Polym. Sci., 1974, 16, 1.
55. Heinrich, G. and Hube, H., Plaste Kautsch., 1986, 33, 88.
56. Sträube, E. and Matzen, D., Kautschuk Gummi. Kunststoffe, 1992, 45, 264.
57. Heinrich, G. and Vilgis, T. A. Macromolecules, 1993, 26, 1109;
58. Heinrich, G. and Vilgis T. A., Kautschuk Gummi, Kunststoffe, 1993, 46, 283.
59. Kaliske, M. and Heinrich, G., Rubb. Chem. Technol., submitted.
60. Simo, J. C. and Taylor, R. L., Computer Methods in Applied Mechanics and Engineering, 1991, 85, 273.
61. Zienkiewicz, O. C. and Taylor, R. L., The Finite Element Method, Vol. l, Basic Formulation and Linear Problems, 4th edn. McGraw-Hill, London, 1989.
62. Zienkiewicz, O. C. and Taylor, R. L., The Finite Element Method, Vol. 2, Solid and Fluid Mechanics, Dynamics and Non-linearity, 4th edn. McGraw-Hill, London, 1991.
63. Flory, J. P., Transactions of the Faraday Society, 1961, 57, 829.
64. Valanis, K. C. and Landel, R. F., Journal Applied Physics, 1967, 38, 2997.
65. Morman, K. N., ASM E, Journal Applied Mechanics, 1986, 53, 726.
66. Miehe, C., Communications in Numerical Methods in Engineering, 1993, 9, 889.
67. Miehe, C., Int. Journal of Numerical Methods in Engineering, 1994,37, 1981.
68. Kalsike, M. and Rothert, H., Engineering Computations, 1997,14, 217.
69. Van den Bogert, P. A. J. and de Borst, R., Archire of Applied Mechanics, 1994, 64, 136.
70. Ogden, R. W., Rubb. Chem. Technol., 1986, 59, 361.
71. Yeoh, O. H., Rubb. Chem. Technol., 1997, 70, 175.
72. Edwards, S. F. and Kerr, J. W., J. Phys. C, 1972, 5, 2289.