[en] This work presents a general framework for constitutive viscoelastic models in the finite deformation regime. The approach is qualified as variational since the constitutive updates consist of a minimization problem within each load increment. The set of internal variables is strain-based and uses a multiplicative decomposition of strain in elastic and viscous components. Spectral decomposition is explored in order to accommodate, into analytically tractable expressions, a wide set of specific models. Moreover, it is shown that, through appropriate choices of the constitutive potentials, the proposed formulation is able to reproduce results obtained elsewhere in the literature. Finally, numerical examples are included to illustrate the characteristics of the present formulation. (C) 2007 Elsevier B.V. All rights reserved.
Anand, L., Weber, G., Finite deformations constitutive equations and a time integration procedure for isotropic hyperelastic-viscoplastic solids (1990) Comput. Methods Appl. Mech. Eng., 79, pp. 173-202
Bonet, J., Large viscoelastic constitutive models (2001) Internat. J. Solids Struct., 38, pp. 2953-2968
Holzapfel, G.A., On large viscoelasticity: continuum formulation and finite element applications to elastomeric structures (1996) Internat. J. Numer. Methods Eng., 39, pp. 3903-3926
Holzapfel, G.A., Gasser, T.C., A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications (2001) Comput. Methods Appl. Mech. Eng., 190, pp. 4379-4403
Holzapfel, G.A., Simo, J., A new viscoelastic constitutitve model for continuous media at finite thermomechanical changes (1996) Internat. J. Solids Struct., 33, pp. 3019-3034
P. Le Tallec, Numerical Analysis of Viscoelastic Problems, vol. 109, Masson, Paris, France, 1993, pp. 223-258
Le Tallec, P., Rahier, C., Kaiss, A., Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation (1993) Comput. Methods Appl. Mech. Eng., 109, pp. 223-258
Lion, A., A constitutive model for carbon filled rubber, experimental investigation and mathematical representations (1996) Continuum Mech. Thermodyn., 8, pp. 153-169
Lubliner, J., A model of rubber viscoelasticity (1985) Mech. Res. Commun., 12, pp. 93-99
Miehe, C., Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals (1996) Internat. J. Numer. Methods Eng., 39, pp. 3367-3390
Ortiz, M., Stainier, L., The variational formulation of viscoplastic constitutive updates (1999) Comput. Meth. Appl. Mech. Eng., 171, pp. 419-444
Radovitzky, R., Ortiz, M., Error estimation and adaptive meshing in strongly nonlinear dynamic problems (1999) Comput. Methods Appl. Mech. Eng., 172, pp. 203-240
Reese, S., Govindjee, S., A theory for finite viscoelasticity and numerical aspects (1998) Internat. J. Solids Struct., 35, pp. 3455-3482
Sidoroff, F., Un modèle viscoélastique non linéaire ave configuration intermédiaire (1974) J. Mécanique, 13, pp. 679-713
Simo, J.C., On a fully three dimensional finite-strain viscoelastic damage model: formulation and computational aspects (1987) Comput. Methods Appl. Mech. Eng., 60, pp. 153-173
Simo, J.C., Taylor, R.L., Quasi incompressible finite elasticity in principal stretches, Continuum basis and numerical algorithms (1991) Comput. Methods Appl. Mech. Eng., 85, pp. 273-310
L. Stainier, Une formulation variationelle des algorithmes de calcul des constraintes pour les modèles élastoviscoplastiques et viscoélastiques en grandes transformations, in: 6ème Colloque National en Calcul des Structures, Giens, France, 2003