Comptes Rendus
A new I1-based hyperelastic model for rubber elastic materials
Comptes Rendus. Mécanique, Volume 338 (2010) no. 1, pp. 3-11.

In this Note, we propose a new hyperelastic model for rubber elastic solids applicable over the entire range of deformations. The underlying stored-energy function is a linear combination of the I1-based strain invariants φ(I1;α)=(I1α3α)/(α3α1), where α is a real number. The predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for a variety of rubbery solids. In addition, the key theoretical and practical strengths of the proposed stored-energy function are discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.12.007
Mots clés : Solids and structures, Finite strain, Non-Gaussian elasticity, Polyconvexity

Oscar Lopez-Pamies 1

1 Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300, USA
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Oscar Lopez-Pamies. A new $ {I}_{1}$-based hyperelastic model for rubber elastic materials. Comptes Rendus. Mécanique, Volume 338 (2010) no. 1, pp. 3-11. doi : 10.1016/j.crme.2009.12.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.12.007/

[1] R.W. Ogden Non-linear Elastic Deformations, Dover Publications, Mineola, New York, 1997

[2] O. Lopez-Pamies An exact result for the macroscopic response of particle-reinforced Neo-Hookean solids, J. Appl. Mech., Volume 77 (2010), p. 021016-1-021016-5

[3] O. Lopez-Pamies; M.I. Idiart An exact result for the macroscopic response of porous Neo-Hookean solids, J. Elasticity, Volume 95 (2009), pp. 99-105

[4] L.R.G. Treloar The elasticity of a network of long-chain molecules–II, Trans. Faraday Soc., Volume 39 (1943), pp. 241-246

[5] V. Vahapoglu; S. Karadeniz Constitutive equations for isotropic rubber-like materials using phenomenological approach: A bibliography (1930–2003), Rubber Chem. Technol., Volume 79 (2003), pp. 489-498

[6] A.N. Gent A new constitutive relation for rubber, Rubber Chem. Technol., Volume 69 (1996), pp. 59-61

[7] R.W. Ogden Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond. A, Volume 326 (1972), pp. 565-584

[8] M.F. Beatty An average-stretch full-network model for rubber elasticity, J. Elasticity, Volume 70 (2003), pp. 65-86

[9] C.O. Horgan; G. Saccomandi A molecular basis for the Gent constitutive model of rubber elasticity, J. Elasticity, Volume 68 (2002), pp. 167-176

[10] E.M. Arruda; M.C. Boyce A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, J. Mech. Phys. Solids, Volume 41 (1993), pp. 389-412

[11] O.H. Yeoh Some forms of the strain energy function for rubber, Rubber Chem. Technol., Volume 66 (1993), pp. 754-771

[12] L.R.G. Treloar Stress-strain data for vulcanised rubber under various types of deformation, Trans. Faraday Soc., Volume 40 (1944), pp. 59-70

[13] L. Meunier; G. Chagnon; D. Favier; L. Orge; P. Vacher Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber, Polymer Testing, Volume 27 (2008), pp. 765-777

[14] N. Lahellec; F. Mazerolle; J.C. Michel Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: Theory and experimental validation, J. Mech. Phys. Solids, Volume 52 (2004), pp. 27-49

[15] M.C. Boyce Direct comparison of the Gent and the Arruda–Boyce constitutive models for rubber elasticity, Rubber Chem. Technol., Volume 69 (1996), pp. 781-785

[16] C.O. Horgan; G. Saccomandi Phenomenological hyperelastic strain-stiffening constitutive models for rubber, Rubber Chem. Technol., Volume 79 (2005), pp. 1-18

[17] J.M. Ball Convexity conditions and existence theorems in nonlinear elasticity, Arch. Ration. Mech. Anal., Volume 63 (1977), pp. 337-403

[18] L. Zee; E. Sternberg Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids, Arch. Ration. Mech. Anal., Volume 83 (1983), pp. 53-90

[19] R.S. Rivlin; D.W. Saunders Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber, Philos. Trans. R. Soc. London A, Volume 243 (1951), pp. 251-288

[20] L.R.G. Treloar The Physics of Rubber Elasticity, Oxford University Press, 2005

[21] E. Pucci; G. Saccomandi A note on the Gent model for rubber-like materials, Rubber Chem. Technol., Volume 75 (2002), pp. 839-851

[22] P.W. Bridgman The compression of sixty-one solid substances to 25.000 kg/cm, determined by a new rapid method, Proc. Am. Acad. Arts Sci., Volume 76 (1945), pp. 9-24

[23] O. Lopez-Pamies; R. Garcia; E. Chabert; J.-Y. Cavaillé; P. Ponte Castañeda Multiscale modeling of oriented thermoplastic elastomers with lamellar morphology, J. Mech. Phys. Solids, Volume 56 (2008), pp. 3206-3223

[24] C. Miehe Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials, Eur. J. Mech. A, Volume 14 (1995), pp. 697-720

[25] R.W. Ogden; R.D. Roxburgh A pseudo-elastic model for the Mullins effect in filled rubber, Proc. R. Soc. Lond. A, Volume 455 (1999), pp. 2861-2877

[26] O. Lopez-Pamies; P. Ponte Castañeda On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I–Theory, J. Mech. Phys. Solids, Volume 54 (2006), pp. 807-830

[27] O. Lopez-Pamies; P. Ponte Castañeda On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. II–Application to cylindrical fibers, J. Mech. Phys. Solids, Volume 54 (2006), pp. 831-863

[28] M. Brun; O. Lopez-Pamies; P. Ponte Castañeda Homogenization estimates for fiber-reinforced elastomers with periodic microstructures, Internat. J. Solids Structures, Volume 44 (2007), pp. 5953-5979

[29] M. Agoras; O. Lopez-Pamies; P. Ponte Castañeda A general hyperelastic model for incompressible fiber-reinforced elastomers, J. Mech. Phys. Solids, Volume 57 (2009), pp. 268-286

[30] O. Lopez-Pamies; P. Ponte Castañeda Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations, J. Elasticity, Volume 76 (2004), pp. 247-287

[31] O. Lopez-Pamies; P. Ponte Castañeda Homogenization-based constitutive models for porous elastomers and implications for microscopic instabilities. I–Analysis, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1677-1701

[32] O. Lopez-Pamies; P. Ponte Castañeda Homogenization-based constitutive models for porous elastomers and implications for microscopic instabilities. II–Results, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1702-1728

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