A molecular-statistical basis for the Gent constitutive model of rubber elasticity

Journal of Elasticity

Volumn 68, Issue 1-3, 2002, Pages 167-176

  Horgan, Cornelius O ^a   Saccomandi, Giuseppe ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

Gent constitutive model; Incompressible rubber; Strain hardening phenomena

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; CONTINUUM MECHANICS; FUNCTIONS; GREEN'S FUNCTION; INCOMPRESSIBLE FLOW; INVERSE PROBLEMS; MOLECULAR DYNAMICS; RUBBER; STATISTICAL METHODS; STRAIN HARDENING;

CAUCHY-GREEN STRAIN TENSOR; GENT CONSTITUTIVE MODEL; INCOMPRESSIBLE RUBBER; LANGEVIN FUNCTIONS; MOLECULAR-STATISTICAL BASIS;

ELASTICITY;

EID: 0242653712     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026029111723     Document Type: Article

References (29)

1. E.M. Arruda and M.C. Boyce, A three-dimensional constitutive model for the large deformation stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41 (1993) 389-412.
2. G.A. Baker and P.R. Graves-Morris, Padè Approximants, 2nd edn. Cambridge Univ. Press, New York (1996).
3. M.F. Beatty, Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues - with examples. Appl. Mech. Rev. 40 (1987) 1699-1733. Reprinted with minor modifications as Introduction to nonlinear elasticity n: M.M. Carroll and M.A. Hayes (eds), Nonlinear Effects in Fluids and Solids. Plenum Press, New York (1996), pp. 16-112.
4. M.F. Beatty, A stretch average full-network model for rubber elasticity. J. Elasticity (in press).
5. M.C. Boyce, Direct comparison of the Gent and Arruda-Boyce constitutive models of rubber elasticity. Rubber Chemistry Technol. 69 (1996) 781-785.
6. M.C. Boyce and E.M. Arruda, Constitutive models of rubber elasticity: A review. Rubber Chemistry Technol. 73 (2000) 504-523.
7. A. Cohen, A Padè approximant to the inverse Langevin function. Rheol. Acta 30 (1991) 270-273.
8. B. Erman and J.E. Mark, Structures and Properties of Rubberlike Networks. Oxford Univ. Press, Oxford (1997).
9. E. Fried, An elementary molecular-statistical basis for the Mooney and Rivlin-Saunders theories of rubber elasticity. J. Mech. Phys. Solids 50 (2002) 571-582.
10. A.N. Gent, A new constitutive relation for rubber. Rubber Chemistry Technol. 69 (1996) 59-61.
11. A.N. Gent, Elastic instabilities of inflated rubber shells. Rubber Chemistry Technol. 72 (1999) 263-268.
12. R.N. Haward, The application of non-Gaussian chain statistics to ultralow density polyethylenes and other thermoplastic elastomers. Polymer 40 (1999) 5821-5832.
13. C.O. Horgan and G. Saccomandi, Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility. J. Elasticity 56 (1999) 159-170.
14. C.O. Horgan and G. Saccomandi, Pure axial shear of isotropic incompressible nonlinearly elastic materials with limiting chain extensibility. J. Elasticity 57 (1999) 307-319.
15. C.O. Horgan and G. Saccomandi, Pure azimuthal shear of isotropic, incompressible hyperelastic materials with limiting chain extensibility. Internat. J. Nonlinear Mech. 36 (2001) 465-475.
16. C.O. Horgan and G. Saccomandi, Large deformations of a rotating solid cylinder for non-Gaussian isotropic, incompressible, hyperelastic materials. J. Appl. Mech. 68 (2001) 115-117.
17. C.O. Horgan and G. Saccomandi, Antiplane shear deformations for non-Gaussian isotropic, incompressible hyperelastic materials. Proc. Roy. Soc. London A 457 (2001) 1999-2017.
18. C.O. Horgan and G. Saccomandi, Constitutive modelling of rubber-like and biological materials with limiting chain extensibility. Math. Mech. Solids 7 (2002) 353-371.
19. C.O. Horgan and G. Saccomandi, Finite thermoelasticity with limiting chain extensibility. J. Mech. Phys. Solids 51 (2003) 1127-1146.
20. C.O. Horgan and G. Saccomandi, Helical shear for hardening generalized neo-Hookean elastic materials. Math. Mech. Solids 8 (2003) (in press).
21. C.O. Horgan and G. Saccomandi, A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomechanics Modeling Mechanobiology 1 (2003) 251-266.
22. C.O. Horgan, G. Saccomandi and I. Sgura, A two-point boundary-value problem for the axial shear of hardening isotropic incompressible nonlinearly elastic materials. SIAM J. Appl. Math. 62 (2002) 1712-1727.
23. H.G. Kilian, Equation of state of real networks. Polymer 22 (1981) 209-217.
24. W. Kuhn and F. Grün, Beziehungen zwischen elastischen Konstanten und Dehnungsdoppel-brechung höchelastischer stoffe. Kolloid. Z. 101 (1942) 248-271.
25. R.W. Ogden, Non-linear Elastic Deformations. Ellis Horwood, Chichester (1984). Reprinted by Dover, New York (1997).
26. G. Perrin, Analytic stress-strain relationship for isotropic network model of rubber elasticity. C. R. Acad. Sci. Paris Sér. II 328 (2000) 5-10.
27. E. Pucci and G. Saccomandi, A note on the Gent model for rubber-like materials. Rubber Chemistry Technol. 75 (2002) 839-851.
28. L.R.G. Treloar, The photoelastic properties of short-chain molecular networks. Trans. Faraday Soc. 50 (1954) 881-896.
29. L.R.G. Treloar, The Physics of Rubber Elasticity, 3rd edn. Oxford Univ. Press, Oxford (1975).