An extended tube-model for rubber elasticity: Statistical-mechanical theory and finite element implementation

Rubber Chemistry and Technology

Volumn 72, Issue 4, 1999, Pages 602-632

  Kaliske, M ^a   Heinrich, G ^b  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b Materials Research ^*  (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ELASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; STATISTICAL MECHANICS; STRAIN;

EXTENDED TUBE-MODEL;

RUBBER;

EID: 0033320084     PISSN: 00359475     EISSN: None     Source Type: Journal    
DOI: 10.5254/1.3538822     Document Type: Article

References (89)

1. K. N. Morman, "Rubber Viscoelasticity - A Review of Current Understanding," Ford Motor Company: Dearborn, Michigan, 1985.
2. M. Kaliske and H. Rothert, Eng. Comput. 14, 217(1997).
3. L. R. G. Treloar, "The Physics of Rubber Elasticity," Clarendon Press, Oxford, 1975.
4. H. G. Kilian, Polymer 22, 209 (1981).
5. H. Ambacher, H.-F. Enderle, H. G. Kilian, and A. Sauter, Prog. Colloid Polym. Sci. 80, 209 (1989).
6. E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 41, 389 (1993).
7. G. Heinrich, E. Straube, and G. Helmis, Adv. Polym. Sci. 85, 33 (1988).
8. S. F. Edwards and T. A. Vilgis, Rep. Prog. Phys. 51, 243 (1988).
9. G. Heinrich and M. Kaliske, Comput. Theor. Polym. Sci., 7, 227 (1997).
10. K. C. Valanis and R. F. Landel, J. Appl. Phys. 38, 2997 (1967).
11. B. Erman and J. E. Mark, "Structure and Properties of Rubberlike Networks," Oxford University Press, Oxford, NY, 1997.
12. K. Dušek and W. Prins, Adv. Polym. Sci. 6, 1 (1969).
13. A. J. Staverman, Adv. Polym. Sci. 44, 73 (1982).
14. J. P. Queslel and J. E. Mark, Adv. Polym. Sci. 65, 135 (1984).
15. T. A. Vilgis, in "Comprehensive Polymer Science," G. Allen, Ed., Pergamon Press, 1989, v. 6.
16. B. E. Eichinger, Annu. Rev. Phys. Chem. 34, 359 (1983).
17. R. Ullman, in "Material Science and Technology," R. W. Cahn, P. Haasen, and E. J. Kramer, Eds., VCH, Weinheim, 1993, v. 12.
18. K. J. Smith, Jr., in "Comprehensive Polymer Science," Second Supplement; G. Allen, Ed., Pergamon Press, 1996.
19. "Elastomeric Polymer Networks," J. E. Mark and B. Erman, Eds., Prentice Hall, Englewood Cliffs, New Jersey, 1992.
20. E. Guth and H. M. James, Ind. Eng. Chem. 33, 624 (1941).
21. H. M. James and E. Guth, Ind. Eng. Chem. 35, 455 (1943).
22. F. T. Wall, J. Chem. Phys. 1943, 11, 527 (1943).
23. L. R. G. Treloar, Trans. Faraday Soc. 39, 241 (1943).
24. P. J. Flory and J. Rehner, Jr., J. Chem. Phys. 11, 512 (1943).
25. G. Ronca and G. Allegra, J. Chem. Phys. 63, 4990 (1975).
26. P. J. Flory, J. Chem. Phys. 66, 5720 (1977).
27. B. Erman and P. J. Flory, J. Chem. Phys. 68, 5363 (1978).
28. S. Kästner, Faserforsch. Textiltechn. 27, 1 (1976).
29. S. Kästner, Acta Polym. 31, 444 (1980).
30. S. Kästner, Colloid Polym. Sci. 259, 499, 508 (1981).
31. B. Erman and L. Monnerie, Macromolecules 15, 800 (1982).
32. G. Marrucci, Macromolecules 14, 434 (1981).
33. R. J. Gaylord, Polym. Eng. Sci. 19, 263 (1979).
34. R. J. Gaylord, Polym. Bull. 8, 325 (1982); R. J. Gaylord and J. F. Douglas, Polym. Bull. 18, 347 (1987); R. J. Gaylord and R., J. F. Douglas, J. Polym. Bull. 23, 529 (1990).
35. R. J. Gaylord, Polym. Bull. 8, 325 (1982); R. J. Gaylord and J. F. Douglas, Polym. Bull. 18, 347 (1987); R. J. Gaylord and R., J. F. Douglas, J. Polym. Bull. 23, 529 (1990).
36. R. J. Gaylord, Polym. Bull. 8, 325 (1982); R. J. Gaylord and J. F. Douglas, Polym. Bull. 18, 347 (1987); R. J. Gaylord and R., J. F. Douglas, J. Polym. Bull. 23, 529 (1990).
37. R. C. Ball, M. Doi, S. F. Edwards, and M. Warner, Polymer 22, 1010 (1981).
38. R. T. Deam and S. F. Edwards, Philos. Trans. R. Soc. London A 280, 317 (1976).
39. S. F. Edwards and T. A. Vilgis, Polymer 27, 483 (1986).
40. G. Heinrich and E. Straube, Acta Polym. 35, 115 (1984).
41. G. Heinrich and E. Straube, Polym. Bull. 17, 247 (1987).
42. E. Straube, V. Urban, W. Pyckhout-Hintzen, and D. Richter, Macromolecules 27, 7681 (1994).
43. E. Straube, V. Urban, W. Pyckhout-Hintzen, D. Richter, and C. W. Glinka, Phys. Rev. Lett. 74, 4464 (1995).
44. W. W. Gronski, W. Hoffmann, G. Simon, A. Wutzler, and E. Straube, RUBBER CHEM. TECHNOL. 65, 63 (1992).
45. D. Matzen and E. Straube, Colloid Polym. Sci. 27, 1 (1992).
46. E. Straube and G. Heinrich, Kautsch. Gummi Kunstst. 44, 734 (1991).
47. M. Klüppel, Progr. Colloid Polym. Sci. 90, 137 (1992).
48. M. Klüppel, J. Appl. Polym. Sci. 48, 1137 (1993).
49. M. Klüppel and G. Heinrich, Macromolecules 27, 3569 (1994).
50. K. Kremer and G. S. Grest, in "MC and MD Simulations in Polymer Science," K. Binder, Ed., Oxford Univ. Press, 1994.
51. S. F. Edwards, Proc. Phys. Soc. 85, 613 (1965).
52. M. Rubinstein and S. Panyukov Macromolecules 30, 8036 (1997).
53. W. W. Graessley and S. F. Edwards, Polymer 22, 1329 (1981).
54. D. Richter, B. Farago, R. Butera, L. J. Fetters, J. Huang, and B. Ewen, Macromolecules 26, 795 (1993).
55. P. J. Flory, Proc. R. Soc. London Ser. A, 351, 351, (1976).
56. W. W. Graessley, Adv. Polym. Sci. 16, 1 (1974).
57. G. Heinrich and T. A. Vilgis, Macromolecules 26, 1109 (1993); G. Heinrich and T. A. Vilgis, Kautsch. Gummi Kunstst. 46, 283 (1993); G. Heinrich and T. A. Vilgis, RUBBER CHEM. TECHNOL. 68, 26 (1995); T. A. Vilgis and G. Heinrich, Macromolecules 27, 7846 (1994).
58. G. Heinrich and T. A. Vilgis, Macromolecules 26, 1109 (1993); G. Heinrich and T. A. Vilgis, Kautsch. Gummi Kunstst. 46, 283 (1993); G. Heinrich and T. A. Vilgis, RUBBER CHEM. TECHNOL. 68, 26 (1995); T. A. Vilgis and G. Heinrich, Macromolecules 27, 7846 (1994).
59. G. Heinrich and T. A. Vilgis, Macromolecules 26, 1109 (1993); G. Heinrich and T. A. Vilgis, Kautsch. Gummi Kunstst. 46, 283 (1993); G. Heinrich and T. A. Vilgis, RUBBER CHEM. TECHNOL. 68, 26 (1995); T. A. Vilgis and G. Heinrich, Macromolecules 27, 7846 (1994).
60. G. Heinrich and T. A. Vilgis, Macromolecules 26, 1109 (1993); G. Heinrich and T. A. Vilgis, Kautsch. Gummi Kunstst. 46, 283 (1993); G. Heinrich and T. A. Vilgis, RUBBER CHEM. TECHNOL. 68, 26 (1995); T. A. Vilgis and G. Heinrich, Macromolecules 27, 7846 (1994).
61. M. Klüppel, J. Appl. Polym. Sci. 48, 1137 (1993).
62. J. Kovac and C. C. Crabb, Macromolecules 19, 1744 (1986).
63. G. Heinrich and W. Beckert, Progr. Colloid Polym. Sci. 1992, 90, 47 (1992).
64. K. F. Freed, Adv. Chem. Phys. 22, 1 (1972).
65. S. F. Edwards, Br. Polym. J. 9, 140 (1977).
66. E. Straube and D. Matzen, Kautsch. Gummi Kunstst. 45, 264 (1992).
67. R. M. Christensen, "Mechanics of Composite Materials," Wiley, New York, 1979.
68. E. Guth aand O. Gold, Phys. Rev. 53, 322 (1938).
69. J. B. Donnet, R. C. Bansal, and M. J. Wang, Eds., "Carbon Black, Science and Technology," Marcel Dekker, New York, 1993.
70. G. Huber, Ph.D. Thesis, University Mainz, Germany, 1997.
71. A. Gabler, Ph.D. Thesis, University Halle-Wittenberg, Germany, 1998.
72. J. C. Simo and R. L. Taylor, Computer Methods in Applied Mechanics and Engineering, 85, 273 (1991).
73. C. Miehe, Int. J. Numer. Methods Eng. 37, 1981 (1994).
74. O. C. Zienkiewicz and R. L. Taylor, "The Finite Element Method. Volume 1: Basic Formulation and Linear Problems," Fourth Edition, McGraw-Hill, London, 1989.
75. O. C. Zienkiewicz and R. L. Taylor, "The Finite Element Method. Volume 2: Solid and Fluid Mechanics, Dynamics and Non-Linearity.," Fourth Edition, McGraw-Hill, London, 1991.
76. K. N. Morman, J. Appl. Mech. 53, 726 (1986).
77. C. Miehe, Communi. Num. Meth. Eng. 9, 889 (1993).
78. R. W. Ogden, "Non-Linear Elastic Deformations," Ellis Horwood, Chichester, 1984.
79. H. P. Schwefel, "Evolution and Optimum Seeking," Wiley, New York, 1995.
80. O. H. Yeoh, RUBBER CHEM. TECHNOL. 70, 175 (1997).
81. O. H. Yeoh, RUBBER CHEM. TECHNOL. 63, 792 (1990).
82. P. A. J. van den Bogert and R. de Burst, Arch. Appl. Mech. 64, 136 (1994).
83. A. J. Marzocca, S. Cerveny, and R. B. Raimondo, J. Appl. Polym. Sci. 66, 1085 (1997).
84. O. H. Yeoh, RUBBER CHEM. TECHNOL. 66, 754 (1993).
85. A. N. Gent. RUBBER CHEM. TECHNOL. 69, 59 (1996).
86. O. H. Yeoh and P. D. Fleming, J. Polym. Sci.: Part B: Polym. Physics 35, 1919 (1997).
87. J. Bastide, C. Picot, and S. Candau, J. Macromol. Sci. Phys. 19, 13 (1981).
88. J.D. Ferry, "Viscoelaslic Properties of Polymers," Third Edition, Wiley, New York, 1980.
89. W. Pyckhout-Hintzen, in preparation.