A new I1-based hyperelastic model for rubber elastic materials

Comptes Rendus - Mecanique

Volumn 338, Issue 1, 2010, Pages 3-11

  Lopez Pamies, Oscar ^a  

^a Stony Brook University   (United States)

Author keywords

Finite strain; Non Gaussian elasticity; Polyconvexity; Solids and structures

Indexed keywords

ELASTIC MATERIALS; ELASTIC SOLIDS; ENERGY FUNCTIONS; EXPERIMENTAL DATA; FINITE STRAIN; HYPERELASTIC MODELS; LINEAR COMBINATIONS; NON-GAUSSIAN ELASTICITY; POLYCONVEXITY; PREDICTIVE CAPABILITIES; REAL NUMBER; STRAIN INVARIANTS;

GAUSSIAN NOISE (ELECTRONIC); NUMBER THEORY; RUBBER;

ELASTICITY;

DEFORMATION; ELASTIC PROPERTY; GAUSSIAN METHOD; RUBBER;

EID: 75249091427     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crme.2009.12.007     Document Type: Article

References (32)

1. Ogden R.W. Non-linear Elastic Deformations (1997), Dover Publications, Mineola, New York
2. Lopez-Pamies O. An exact result for the macroscopic response of particle-reinforced Neo-Hookean solids. J. Appl. Mech. 77 (2010) 021016-1-021016-5
3. Lopez-Pamies O., and Idiart M.I. An exact result for the macroscopic response of porous Neo-Hookean solids. J. Elasticity 95 (2009) 99-105
4. Treloar L.R.G. The elasticity of a network of long-chain molecules-II. Trans. Faraday Soc. 39 (1943) 241-246
5. Vahapoglu V., and Karadeniz S. Constitutive equations for isotropic rubber-like materials using phenomenological approach: A bibliography (1930-2003). Rubber Chem. Technol. 79 (2003) 489-498
6. Gent A.N. A new constitutive relation for rubber. Rubber Chem. Technol. 69 (1996) 59-61
7. Ogden R.W. Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. A 326 (1972) 565-584
8. Beatty M.F. An average-stretch full-network model for rubber elasticity. J. Elasticity 70 (2003) 65-86
9. Horgan C.O., and Saccomandi G. A molecular basis for the Gent constitutive model of rubber elasticity. J. Elasticity 68 (2002) 167-176
10. Arruda E.M., and Boyce M.C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41 (1993) 389-412
11. Yeoh O.H. Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66 (1993) 754-771
12. Treloar L.R.G. Stress-strain data for vulcanised rubber under various types of deformation. Trans. Faraday Soc. 40 (1944) 59-70
13. Meunier L., Chagnon G., Favier D., Orge L., and Vacher P. Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber. Polymer Testing 27 (2008) 765-777
14. Lahellec N., Mazerolle F., and Michel J.C. Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: Theory and experimental validation. J. Mech. Phys. Solids 52 (2004) 27-49
15. Boyce M.C. Direct comparison of the Gent and the Arruda-Boyce constitutive models for rubber elasticity. Rubber Chem. Technol. 69 (1996) 781-785
16. Horgan C.O., and Saccomandi G. Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chem. Technol. 79 (2005) 1-18
17. Ball J.M. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63 (1977) 337-403
18. Zee L., and Sternberg E. Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids. Arch. Ration. Mech. Anal. 83 (1983) 53-90
19. Rivlin R.S., and Saunders D.W. Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber. Philos. Trans. R. Soc. London A 243 (1951) 251-288
20. Treloar L.R.G. The Physics of Rubber Elasticity (2005), Oxford University Press
21. Pucci E., and Saccomandi G. A note on the Gent model for rubber-like materials. Rubber Chem. Technol. 75 (2002) 839-851
22. Bridgman P.W. The compression of sixty-one solid substances to 25.000 kg/cm, determined by a new rapid method. Proc. Am. Acad. Arts Sci. 76 (1945) 9-24
23. Lopez-Pamies O., Garcia R., Chabert E., Cavaillé J.-Y., and Ponte Castañeda P. Multiscale modeling of oriented thermoplastic elastomers with lamellar morphology. J. Mech. Phys. Solids 56 (2008) 3206-3223
24. Miehe C. Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials. Eur. J. Mech. A 14 (1995) 697-720
25. Ogden R.W., and Roxburgh R.D. A pseudo-elastic model for the Mullins effect in filled rubber. Proc. R. Soc. Lond. A 455 (1999) 2861-2877
26. Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I-Theory. J. Mech. Phys. Solids 54 (2006) 807-830
27. Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. II-Application to cylindrical fibers. J. Mech. Phys. Solids 54 (2006) 831-863
28. Brun M., Lopez-Pamies O., and Ponte Castañeda P. Homogenization estimates for fiber-reinforced elastomers with periodic microstructures. Internat. J. Solids Structures 44 (2007) 5953-5979
29. Agoras M., Lopez-Pamies O., and Ponte Castañeda P. A general hyperelastic model for incompressible fiber-reinforced elastomers. J. Mech. Phys. Solids 57 (2009) 268-286
30. Lopez-Pamies O., and Ponte Castañeda P. Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations. J. Elasticity 76 (2004) 247-287
31. Lopez-Pamies O., and Ponte Castañeda P. Homogenization-based constitutive models for porous elastomers and implications for microscopic instabilities. I-Analysis. J. Mech. Phys. Solids 55 (2007) 1677-1701
32. Lopez-Pamies O., and Ponte Castañeda P. Homogenization-based constitutive models for porous elastomers and implications for microscopic instabilities. II-Results. J. Mech. Phys. Solids 55 (2007) 1702-1728