On computational issues in large deformation analysis of rubber bushings

Mechanics of Structures and Machines

Volumn 25, Issue 3, 1997, Pages 287-309

  Chen, Jiun Shyan ^a   Wu, Cheng Tang ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; ELASTIC MODULI; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; RUBBER PRODUCTS; SHEAR DEFORMATION; STRAIN;

RUBBER BUSHINGS; STRAIN ENERGY DENSITY FUNCTIONS;

BUSHINGS;

EID: 0031198819     PISSN: 08905452     EISSN: None     Source Type: Journal    
DOI: 10.1080/08905459708905291     Document Type: Article

References (34)

1. A. N. Gent and P. B. Lindley, The compression of bonded rubber blocks, Proceedings of the Institution of Mechanical Engineers 173: 111-122 (1959).
2. A. N. Gent and E. A. Meinecke, Compression, bending and shear of bonded rubber blocks, Polymer Engineering and Science 10: 48-53 (1970).
3. A. R. Payne, Dynamic properties of vulcanized rubber: 5, Shape Factors and Functions in Rubber Engineering, Research Association of British Rubber Manufacturers, Research Report No. 84, Shawbury (1957).
4. E. F. Göbel, Rubber Springs Design, (Transl. A. M. Brichter), Newnes-Burterworth, London, 1974.
5. L. R. Herrmann, Elasticity equations for incompressible and nearly incompressible materials by a variational theorem, AIAA J. 3: 1896-1900 (1965).
6. S. W. Key, A variational principle for incompressible and nearly incompressible anisotropic elasticity, Int. J. Solids Struct. 5: 951-964 (1969).
7. P. Tong, An assumed stress hybrid finite element method for an incompressible and nearly-incompressible material, Int. J. Solids Struct. 5: 455-161 (1969).
8. W. K. Liu, T. Belytschko, and J. S. Chen, Nonlinear versions of flexurally superconvergent elements, Comput. Meth. Appl. Mech. Engng. 71: 241-256 (1988).
9. I. Babuska, The finite element method with Lagrangian multipliers, Numer. Math. 20: 179-192 (1973)
10. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers, RAIRO Anal. Numer. 8: 129-151 (1975)
11. D. S Malkas and T. J. R. Hughes, Mixed finite element methods-reduced and selective integration techniques: A unification of concepts, Comput. Meth. Appl. Mech. Engng 15: 63-81 (1978).
12. W. K. Liu, J. S.-J. Ong, and R. A. Uras, Finite element stabilization matrices - A unification approach, Comput. Meth. Appl. Mech. Engng. 53: 13-46 (1986).
13. J. S. Chen, K. Satyamurthy, and L. R. Hirschfelt, Consistent finite element procedures for nonlinear rubber elasticity with a higher order strain energy function, Comput. & Struct 50: 715-727 (1994).
14. J. S. Chen, C. Pan, and C. T. Wu, A pressure projection method for nearly incompressible rubber hyperelasticity, Part I: Theory, Journal of Applied Mechanics 63(4): 862-868 (1996).
15. J. S. Chen, C. T. Wu, and C. Pan, A pressure projection method for nearly incompressible rubber hyperelasticity, Part II: Application, Journal of Applied Mechanics 63(4): 869-876 (1996).
16. J. S. Chen, C. Pan, and T. Y. P. Chang, On the control of pressure oscillation in bilinear-displacement constant-pressure element, Comput. Meth. Appl. Mech. Engng. 128: 137-152 (1995).
17. T. Y. P. Chang, A. F Saleeb, and G. Li, Large strain analysis of rubber-like materials based on a perturbed Lagrangian variational principle, Computational Mechanics 8: 221-233 (1991).
18. J. S. Chen, W. Han, C. T. Wu, and W. Duan, On the perturbed Lagrangian formulation for nearly incompressible and incompressible hyperelasticity, Computer Methods in Applied Mechanics and Engineering 142, 335-351 (1997).
19. R. S. Rivlin, Large elastic deformation of isotropic materials, Part VI: Further results in the theory of torsion, shear and flexure, Philosophical Transactions of the Royal Society of London A242: 173-195 (1949).
20. K. C. Valanis and R. F. Landel, The strain energy function of a hyperelastic material in terms of the extension ratios, J. Appl. Phys. 38: 2997-3002 (1967).
21. R. W. Ogden, Large deformation isotropic elasticity - on the correlation of theory and experiment for compressible rubber-like solids, Proc. Rheology Soc., London, Serial A, A328: 567-583 (1972).
22. P. J. Blatz and W. L. Ko, Application of finite elastic theory to the deformation of rubbery materials, Trans. Soc. Rheol. 6: 223-251 (1962).
23. N. W. Tschoegl, Constitutive equations for elastomers, J. Polymer Sci. A1: 1959-1970 (1971).
24. A. G. James, A. Green, and G. M. Simpson, Strain energy functions of rubber. I. Characterization of gum rubber, J. Appl. Polymer Sci. 19: 2033-2058 (1975).
25. A. G. James and A. Green, Strain energy functions of rubber. II. The characterization of filled vulcanizates, J. Appl. Polymer Sci. 19: 2319-2330 (1975).
26. W. Seki, Y. Fukaheri, Y. Iseda, and T. Matsunaga, A large-deformation finite element analysis for multi-layer elascomeric bearings, Rubb. Chem. Technol. 60: 856-869 (1987).
27. S. Kawabata and H. Kawai, Strain energy density functions for rubber vulcanizates from biaxial extension, Advances in Polymer Sci. 24: 89-124 (1977).
28. O. H. Yeoh, Characterization of elastic properties of carbon black filled rubber vulcanizates, Rubber Chemistry and Technology 63: 792-805 (1990).
29. M. Mooney, A theory of large elastic deformation, Journal of Applied Physics 11: 582-592 (1940).
30. R. S. Rivlin, Rheology theory and applications, [ed. F. R. Eirich], Academic Press, New York, 1(10): 351-385 (1956).
31. 2, Journal of the National Bureau of Standard - A. Physics and Chemistry 68A(4): 259-268 (1964).
32. R. W. Penn, Volume changes accompanying the extension of rubber, transactions of the society of theology 14(4): 509-517 (1970).
33. O H Yeoh, personal communication, 1994.
34. A. C. Stevenson, Some boundary problems of two-dimensional elasticity, Philos. Mag. 34: 766-793 (1943).