Comptes Rendus
On the two-potential constitutive modeling of rubber viscoelastic materials
Comptes Rendus. Mécanique, Volume 344 (2016) no. 2, pp. 102-112.

This Note lays out the specialization of the two-potential constitutive framework — also known as the “generalized standard materials” framework — to rubber viscoelasticity. Inter alia, it is shown that a number of popular rubber viscoelasticity formulations, introduced over the years following different approaches, are special cases of this framework. As a first application of practical relevance, the framework is utilized to put forth a new objective and thermodynamically consistent rubber viscoelastic model for incompressible isotropic elastomers. The model accounts for the non-Gaussian elasticity of elastomers, as well as for the deformation-enhanced shear thinning of their viscous dissipation governed by reptation dynamics. The descriptive and predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for two commercially significant elastomers.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.11.004
Mots clés : Finite deformations, Internal variables, Dissipative solids, Soft solids

Aditya Kumar 1 ; Oscar Lopez-Pamies 1

1 Department of Civil and Environmental Engineering, University of Illinois, Urbana–Champaign, IL 61801, USA
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Aditya Kumar; Oscar Lopez-Pamies. On the two-potential constitutive modeling of rubber viscoelastic materials. Comptes Rendus. Mécanique, Volume 344 (2016) no. 2, pp. 102-112. doi : 10.1016/j.crme.2015.11.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.11.004/

[1] A.E. Green; R.S. Rivlin The mechanics of non-linear materials with memory, Arch. Ration. Mech. Anal., Volume 1 (1957), pp. 1-21

[2] A.C. Pipkin; T.G. Rogers A nonlinear integral representation for viscoelastic behavior, J. Mech. Phys. Solids, Volume 16 (1968), pp. 59-72

[3] F.J. Lockett Nonlinear Viscoelastic Solids, Academic Press, London, New York, 1972

[4] F. Sidoroff Un modèle viscoélastique non linéaire avec configuration intermédiaire, J. Méc., Volume 13 (1974), pp. 679-713

[5] P. Le Tallec; C. Rahier; A. Kaiss Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation, Comput. Methods Appl. Mech. Eng., Volume 109 (1993), pp. 233-258

[6] S. Reese; S. Govindjee A theory of finite viscoelasticity and numerical aspects, Int. J. Solids Struct., Volume 35 (1998), pp. 3455-3482

[7] J.S. Bergström; M.C. Boyce Constitutive modeling of the large strain time-dependent behavior of elastomers, J. Mech. Phys. Solids, Volume 46 (1998), pp. 931-954

[8] C. Miehe; S. Göktepe A micro–macro approach to rubber-like materials, part II: the micro-sphere model of finite rubber viscoelasticity, J. Mech. Phys. Solids, Volume 53 (2005), pp. 2231-2258

[9] C. Linder; M. Tkachuk; C. Miehe A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity, J. Mech. Phys. Solids, Volume 59 (2011), pp. 2134-2156

[10] B.D. Coleman; M.E. Gurtin Thermodynamics with internal state variables, J. Chem. Phys., Volume 47 (1967), pp. 597-613

[11] H. Ziegler An attempt to generalize Onsager's principle, and its significance for rheological problems, Z. Angew. Math. Phys., Volume 9b (1958), pp. 748-763

[12] B. Halphen; Q.S. Nguyen Sur les matériaux standard généralisés, J. Méc., Volume 14 (1975), pp. 39-63

[13] P. Germain; Q.S. Nguyen; P. Suquet Continuum thermodynamics, J. Appl. Mech., Volume 50 (1983), pp. 1010-1020

[14] H. Ziegler; C. Wehrli The derivation of constitutive relations from the free energy and the dissipation function, Adv. Appl. Mech., Volume 25 (1987), pp. 183-238

[15] K. Hackl Generalized standard media and variational principles in classical and finite strain elastoplasticity, J. Mech. Phys. Solids, Volume 45 (1997), pp. 667-688

[16] B. Bourdin; G.A. Francfort; J.-J. Marigo The variational approach to fracture, J. Elast., Volume 91 (2008), pp. 5-148

[17] A. Mielke A mathematical framework for standard generalized materials in the rate-independent case (R. Helmig; A. Mielke; B. Wohlmuth, eds.), Multifield Problems in Fluid and Solid Mechanics, Lecture Notes in Applied and Computational Mechanics, vol. 28, 2006, pp. 399-428

[18] L. Laiarinandrasana; R. Piques; A. Robisson Visco-hyperelastic model with internal state variable coupled with discontinuous damage concept under total Lagrangian formulation, Int. J. Plast., Volume 19 (2003), pp. 977-1000

[19] J.M. Martinez; A. Boukamel; S. Meo; S. Lejeunes Statistical approach for a hyper-visco-plastic model for filled rubber: experimental characterization and numerical modeling, Eur. J. Mech. A, Solids, Volume 30 (2011), pp. 1028-1039

[20] 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

[21] O. Lopez-Pamies A new I1-based hyperelastic model for rubber elastic materials, C. R., Méc., Volume 338 (2010), pp. 3-11

[22] S.F. Edwards Statistical mechanics with topological constraints, I, Proc. Phys. Soc., Volume 91 (1967), pp. 513-519

[23] P.G. de Gennes Reptation of a polymer chain in the presence of fixed obstacles, J. Chem. Phys., Volume 55 (1971), pp. 572-579

[24] M. Doi; S.F. Edwards The Theory of Polymer Dynamics, Oxford University Press, New York, 1998

[25] A.N. Gent Relaxation processes in vulcanized rubber, I: relation among stress relaxation, creep, recovery, and hysteresis, J. Appl. Polym. Sci., Volume 6 (1962), pp. 433-441

[26] A.N. Gent Relaxation processes in vulcanized rubber, II: secondary relaxation due to network breakdown, J. Appl. Polym. Sci., Volume 6 (1962), pp. 442-448

[27] A.S. Khan; O. Lopez-Pamies Time and temperature dependent response and relaxation of a soft polymer, Int. J. Plast., Volume 18 (2002), pp. 1359-1372

[28] A.F.M.S. Amin; A. Lion; S. Sekita; Y. Okui Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: experimental identification and numerical verification, Int. J. Plast., Volume 22 (2006), pp. 1610-1657

[29] J.C. Simo Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Methods Appl. Mech. Eng., Volume 99 (1992), pp. 61-112

[30] J.D. Lawson An order five Runge–Kutta process with extended region of stability, SIAM J. Numer. Anal., Volume 3 (1966), pp. 593-597

[31] N. Lahellec; P. Suquet On the effective behavior of nonlinear inelastic composites, I: incremental variational principles, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1932-1963

[32] T. Goudarzi; D.W. Spring; G.H. Paulino; O. Lopez-Pamies Filled elastomers: a theory of filler reinforcement based on hydrodynamic and interphasial effects, J. Mech. Phys. Solids, Volume 80 (2015), pp. 37-67

[33] C. Creton; J. Hooker; K.R. Shull Bulk and interfacial contributions to the debonding mechanisms of soft adhesives: extension to large strains, Langmuir, Volume 17 (2001), pp. 4948-4954

[34] O. Lopez-Pamies; M.I. Idiart; T. Nakamura Cavitation in elastomeric solids, I: a defect-growth theory, J. Mech. Phys. Solids, Volume 59 (2011), pp. 1464-1487

[35] M. Hossain; D.K. Vu; P. Steinmann Experimental study and numerical modelling of VHB 4910 polymer, Comput. Mater. Sci., Volume 59 (2012), pp. 65-74

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