On the two-potential constitutive modeling of rubber viscoelastic materials

Green, 1957, The mechanics of non-linear materials with memory, Arch. Ration. Mech. Anal., 1, 1, 10.1007/BF00297992 Pipkin, 1968, A nonlinear integral representation for viscoelastic behavior, J. Mech. Phys. Solids, 16, 59, 10.1016/0022-5096(68)90016-1 Lockett, 1972 Sidoroff, 1974, Un modèle viscoélastique non linéaire avec configuration intermédiaire, J. Méc., 13, 679 Le Tallec, 1993, Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation, Comput. Methods Appl. Mech. Eng., 109, 233, 10.1016/0045-7825(93)90080-H Reese, 1998, A theory of finite viscoelasticity and numerical aspects, Int. J. Solids Struct., 35, 3455, 10.1016/S0020-7683(97)00217-5 Bergström, 1998, Constitutive modeling of the large strain time-dependent behavior of elastomers, J. Mech. Phys. Solids, 46, 931, 10.1016/S0022-5096(97)00075-6 Miehe, 2005, A micro–macro approach to rubber-like materials, part II: the micro-sphere model of finite rubber viscoelasticity, J. Mech. Phys. Solids, 53, 2231, 10.1016/j.jmps.2005.04.006 Linder, 2011, A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity, J. Mech. Phys. Solids, 59, 2134, 10.1016/j.jmps.2011.05.005 Coleman, 1967, Thermodynamics with internal state variables, J. Chem. Phys., 47, 597, 10.1063/1.1711937 Ziegler, 1958, An attempt to generalize Onsager's principle, and its significance for rheological problems, Z. Angew. Math. Phys., 9b, 748, 10.1007/BF02424793 Halphen, 1975, Sur les matériaux standard généralisés, J. Méc., 14, 39 Germain, 1983, Continuum thermodynamics, J. Appl. Mech., 50, 1010, 10.1115/1.3167184 Ziegler, 1987, The derivation of constitutive relations from the free energy and the dissipation function, Adv. Appl. Mech., 25, 183, 10.1016/S0065-2156(08)70278-3 Hackl, 1997, Generalized standard media and variational principles in classical and finite strain elastoplasticity, J. Mech. Phys. Solids, 45, 667, 10.1016/S0022-5096(96)00110-X Bourdin, 2008, The variational approach to fracture, J. Elast., 91, 5, 10.1007/s10659-007-9107-3 Mielke, 2006, A mathematical framework for standard generalized materials in the rate-independent case, vol. 28, 399 Laiarinandrasana, 2003, Visco-hyperelastic model with internal state variable coupled with discontinuous damage concept under total Lagrangian formulation, Int. J. Plast., 19, 977, 10.1016/S0749-6419(02)00089-X Martinez, 2011, Statistical approach for a hyper-visco-plastic model for filled rubber: experimental characterization and numerical modeling, Eur. J. Mech. A, Solids, 30, 1028, 10.1016/j.euromechsol.2011.06.013 Arruda, 1993, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, J. Mech. Phys. Solids, 41, 389, 10.1016/0022-5096(93)90013-6 Lopez-Pamies, 2010, A new I1-based hyperelastic model for rubber elastic materials, C. R., Méc., 338, 3, 10.1016/j.crme.2009.12.007 Edwards, 1967, Statistical mechanics with topological constraints, I, Proc. Phys. Soc., 91, 513, 10.1088/0370-1328/91/3/301 de Gennes, 1971, Reptation of a polymer chain in the presence of fixed obstacles, J. Chem. Phys., 55, 572, 10.1063/1.1675789 Doi, 1998 Gent, 1962, Relaxation processes in vulcanized rubber, I: relation among stress relaxation, creep, recovery, and hysteresis, J. Appl. Polym. Sci., 6, 433, 10.1002/app.1962.070062207 Gent, 1962, Relaxation processes in vulcanized rubber, II: secondary relaxation due to network breakdown, J. Appl. Polym. Sci., 6, 442, 10.1002/app.1962.070062208 Khan, 2002, Time and temperature dependent response and relaxation of a soft polymer, Int. J. Plast., 18, 1359, 10.1016/S0749-6419(02)00003-7 Amin, 2006, 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., 22, 1610, 10.1016/j.ijplas.2005.09.005 Simo, 1992, Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Methods Appl. Mech. Eng., 99, 61, 10.1016/0045-7825(92)90123-2 Lawson, 1966, An order five Runge–Kutta process with extended region of stability, SIAM J. Numer. Anal., 3, 593, 10.1137/0703051 Lahellec, 2007, On the effective behavior of nonlinear inelastic composites, I: incremental variational principles, J. Mech. Phys. Solids, 55, 1932, 10.1016/j.jmps.2007.02.003 Goudarzi, 2015, Filled elastomers: a theory of filler reinforcement based on hydrodynamic and interphasial effects, J. Mech. Phys. Solids, 80, 37, 10.1016/j.jmps.2015.04.012 Creton, 2001, Bulk and interfacial contributions to the debonding mechanisms of soft adhesives: extension to large strains, Langmuir, 17, 4948, 10.1021/la010117g Lopez-Pamies, 2011, Cavitation in elastomeric solids, I: a defect-growth theory, J. Mech. Phys. Solids, 59, 1464, 10.1016/j.jmps.2011.04.015 Hossain, 2012, Experimental study and numerical modelling of VHB 4910 polymer, Comput. Mater. Sci., 59, 65, 10.1016/j.commatsci.2012.02.027