Modeling the stress-strain behavior of rubber

Rubber Chemistry and Technology

Volumn 78, Issue 3, 2005, Pages 391-425

  Muhr, A H ^a  

^a Rubber Consultants   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; RUBBER; STRESS RELAXATION;

ANALYTICAL EXPRESSIONS; CYCLIC STRESS RELAXATIONS; ELASTICITY THEORY; INELASTIC EFFECTS; MATHEMATICAL STRUCTURE; PRACTICAL PROBLEMS; STRESS-STRAIN BEHAVIORS; THREE-DIMENSIONAL MODEL;

FINITE ELEMENT METHOD;

EID: 34247097385     PISSN: 00359475     EISSN: None     Source Type: Journal    
DOI: 10.5254/1.3547890     Document Type: Article

References (99)

1. L. R. G. Treloar, "The Physics of Rubber Elasticity," 3rd Ed., Clarendon Press, Oxford, 1975.
2. O. H. Yeoh, RUBBER CHEM. TECHNOL. 66, 754 (1990).
3. P. Raos, Plast. Rubber Compos. 19, 293, (1993).
4. D. J. Charlton & J. Yang, RUBBER CHEM. TECHNOL. 67, 481 (1994).
5. M. C. Boyce and E. M. Arruda, RUBBER CHEM. TECHNOL. 73, 506 (2000).
6. D. J. Seibert and N. Schöche, RUBBER CHEM. TECHNOL. 73, 366 (2000).
7. BS 903-5, Physical testing of rubber-Part 5: Guide to the application of rubber testing to FEA, British Standards Institution (2004).
8. "Constitutive Models for Rubber," A. Dorfmann and A. H. Muhr, Eds., Balkema, Rotterdam, 1999.
9. "Constitutive Models for Rubber II," D. Besdo, J. Ihlemann and R. H. Schuster, Eds., Balkema, Lisse, 2001.
10. "Constitutive Models for Rubber III," J. J. C. Busfield and A. H. Muhr, Eds., Balkema, Lisse, 2003.
11. "Constitutive Models for Rubber IV," P-E. Austrell and L. Kari, Eds., Balkema, Lisse, 2005.
12. P. Haupt, "Continuum mechanics and theory of materials", Springer-Verlag, Berlin, 2000.
13. C. Miehe and J. Keck, J. Mech. Phys. Solids 48, 323 (2000).
14. W. Chen and A. F. Saleeb, "Constitutive Equations for Engineering Materials, Vol. 1, Elasticity and Modeling", Wiley, New York, 1982.
15. J. Bonet and R. D. Wood, "Nonlinear Continuum Mechanics for EEA," Cambridge University Press, New York, 1997.
16. J. D. Ferry, "Viscoelastic Properties of Polymers," 2nd Ed., Wiley, New York, 1970.
17. J. E. Adkins and A. N. Gent, Brit. J. Appl. Phys. 5, 354 (1954).
18. Y. Ling and P. A. Engel, RUBBER CHEM. TECHNOL. 65, 917 (1992).
19. Y. Ling, P. A. Engel and Brodsky, J. Eng. Mech. 121, 661 (1995).
20. A. H. Muhr, G. H. Tan and A. G. Thomas, J. Nat. Rubber Res. 3, 261 (1988).
21. K. Papoulia and J. Kelly, J. Eng. Mech. 122, 163 (1996).
22. J. J. C. Busfield and A. G. Thomas, RUBBER CHEM. TECHNOL. 72, 876 (1999).
23. A. N. Gent, Trans. Inst. Rubber Ind. 34, 46 (1958).
24. E. R. Schwarzl and L. C. E. Struik, Adv. Mol. Relaxation Processes 1, 201 (1967).
25. M. L. Williams, R. F. Landel and J. D. Ferry, J. Am. Chem. Soc. 77, 3701 (1955).
26. A. J. M. Spencer, "Continuum Mechanics", Longman (1980).
27. R. W. Ogden, "Non-Linear Elastic Deformation," Wiley, Chicester, UK (1984).
28. S. G. A. Holzapfel, "Nonlinear Solid Mechanics," Wiley, Chicester, UK (2001).
29. R. S. Rivlin and D. W. Saunders, Phil. Trans. R. Soc. A241, 379 (1948).
30. I. C. Criscione, J. D. Humphrey, A. S. Douglas, and W. C. Hunter, J. Mech. Phys. Solids 48, 2445 (2000).
31. J. C. Criscione, J. Elasticity 70, 129 (2003).
32. R. S. Rivlin, Philos. Trans. Soc. 240, 459 (1948).
33. J. E. Bischoff, E. M. Arrada, and K. Grosch, RUBBER CHEM. TECHNOL. 74, 541 (2001).
34. R. W. Penn, Trans. Soc. Rheol. 14, 590 (1970).
35. J. Gough, I. H. Gregory and A. H. Muhr; "Determination of the Constitutive Equations for Vulcanised Rubber;" in "Finite Element Analysis of Elastomers," D. Boast and V. A. Coveney, Eds., Prof. Eng. Publ. Ltd, London, 1999.
36. W. Ehlers and G. Eipper, Acta Mech. 130, 17 (1998).
37. A. N. Gent and P. B. Lindley, Proc. Roy. Soc. A249, 195 (1958).
38. A. Dorfmann, K. N. G. Fuller and R. W. Ogden, ECCMRIII 253 (2003).
39. E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 41, 389 (1993).
40. A. N. Gent, RUBBER CHEM. TECHNOL. 69, 59 (1996).
41. O. H. Yeoh and P. D. Fleming, J. Polym. Sci. B35, 1919 (1997).
42. G. Chagnon, G. Marckmann, and E. Verron, RUBBER CHEM. TECHNOL. 77, 724 (2004).
43. S. F. Edwards and T. Vilgis, Polymer 27, 483 (1986).
44. J. S. Bergström and M. C. Boyce, RUBBER CHEM. TECHNOL. 72, 633 (1999).
45. L. Mullins and N. R. Tobin, J. Appl. Polym. Sci. 9, 2993 (1965).
46. E. Guth and O. Gold, Phys. Rev. 53, 322 (1938).
47. E. Guth, J. Appl. Phys. 16, 20 (1945).
48. M. J. Gregory, Plast. Rubber: Mat. Appl. 4, 184 (1979).
49. 10, 157 (2003).
50. C. K. L. Davies, D. K. De and A. G. Thomas, RUBBER CHEM. TECHNOL. 67, 716 (1994).
51. O. H. Yeoh, RUBBER CHEM. TECHNOL. 63, 792 (1990).
52. A. N. Gent, Proc. Phys. Soc. B65, 487 (1952).
53. C. O. Horgan and Saccomandi, J. Elasticity 56, 159 (1999).
54. 8, 65 (1999).
55. 9, 45 (2001).
56. J. C. Simo, Comput. Meth. Appl. Mech. Eng. 60, 153 (1987).
57. M. J. Gregory, C. Metherell and J. F. Smith, Plast. Rubber, Mater. Appl. 3, 37 (1978).
58. A. N. Gent, J. Appl. Polym. Sci. 6, 433 (1962).
59. 9, 173 (2001).
60. 8, 23 (1999).
61. R. W. Ogden and D. Roxburgh, Proc. Soc. Land. A455, 2861 (1999).
62. A. E. Zuńiga and M. F. Beatty, Z. Angew, Math. Phys. 53, 794 (2002).
63. S. Govindjee and J. C. Simo, J. Mech Phys. Solids 39, 87 (1991).
64. S. Govindjee and J. C. Simo; J. Solids Struct. 29, 1737 (1992).
65. C. Miehe, Euro. J. Mech. 14, 697 (1995).
66. 8, 151 (1999).
67. 10, 237 (2003).
68. W. V. Mars, Tire Science Technol. 32, 120 (2004).
69. 10, 223 (2003).
70. M. Klüppel and J. Schramm, Macromol. Theory Simul. 9, 742 (2000).
71. 8, 189 (2001).
72. W. P. Fletcher & A. N. Gent, Trans. Inst. Rubber Ind. 29, 266 (1953).
73. A. R. Payne, J. Appl. Polym. Sci. 6, 57 (1962).
74. J. S. Bergstrom and M. C. Boyce, J. Mech. Phys. Solids 46, 931 (1998).
75. J. S. Bergström and M. C. Boyce, Mechs. Materials 32, 627, (2000).
76. J. S. Bergström and M. C. Boyce, Mechs. Materials 33, 523, (2001).
77. A. Lion, C. Kardelky and P. Haupt, RUBBER CHEM. TECHNOL. 76, 533 (2003).
78. A. Lion and C. Kardelky, J. Plasticity 20, 1313 (2004).
79. 9, 231 (2001).
80. 10, 357 (2003).
81. D. Besdo and J. Ihlemann, Int. J. Plasticity 19, 1019 (2003).
82. M. Kaliske and H. Rothert, Int. J. Solids Struct. 35, 2057 (1998).
83. K. N. Morman and J. G. Nagtegaal, Int. J. Numer. Methods Eng. 19, 1079 (1983).
84. B. K. Kim and S. K. Youn, Archive Appl. Mech. 71, 748 (2001).
85. 9, 73 (2001).
86. G. Kraus, J. Appl. Polym. Sci. 39, 75 (1984).
87. J. D. Ulmer, RUBBER CHEM. TECHNOL. 69, 15 (1996).
88. G. Heinrich and M. Klüppel, Adv. Polym. Sci. 160, 1 (2002).
89. J. A. Greenwood, H. Minshall and D. Tabor, Proc. Soc. London, 259A, 480 (1961).
90. 8, 13 (1999).
91. M. R. Gurvich, A. T. Andonian and C. Shaw, Tire Sci. Technol. 30, 34 (2002).
92. V. Kerchman and C. Shaw, RUBBER CHEM. TECHNOL. 76, 386 (2003).
93. 10, 309 (2003).
94. A. N. Gent, Brit. J. Appl. Phys. 11, 165 (1960).
95. 8, 65 (1999).
96. C. G. Li and P. S. Steif, RUBBER CHEM. TECHNOL. 73, 193 (2000).
97. 10, 203 (2003).
98. 10, 213 (2003).
99. J. G. R. Kingston, to be published.