A direct numerical integration scheme for visco-hyperelastic models using radial return relaxation
DOI:
https://doi.org/10.13052/EJCM.19.129-140Keywords:
radial return relaxation, visco-hyperelasticity, finite element methodAbstract
In this paper, a numerical integration scheme of the evolution laws for viscohyperelastic models is proposed. The starting points of the method are the exponential mapping (Reese et al., 1998) and the radial return (Weber et al., 1990; Simo, 1988). The originality of this work lies in the substitution of a differential tensorial system by a scalar one with two equations and two unknowns and in a first order Taylor expansion of them. In this way an analytical approximated exponential solution is finally obtained.
Downloads
References
Areias P., Matouš K., “ Finite element formulation for modeling nonlinear viscoelastic elastomers”,
Computer Methods in Applied Mechanics and Engineering, vol. 197, p. 4702-
, 2008.
Fancello E., Vassoler J., Stainier L., “ A variational constitutive update algorithm for a set
of isotropic hyperelastic-viscoplastic material models”, Computer Methods in Applied Mechanics
and Engineering, vol. 197, p. 4132-4148, 2008.
Fehlberg E., “ Low-order classical runge-kutta formulas with step size control and their application
to some heat transfer problems.”, Tech. rep.,NASA TR, vol. R-, p. 315, 1969.
Foerch R., Besson J., Cailletaud G., Pivlin P., “ Polymorphic constitutive equations in finite
element codes”, Comput. Methods Appl. Mech. Engrg., vol. 141, p. 355-372, 1996.
Iserles. A., Marthinsen A., Nørsett S., “ On the implementation of the method of magnus series
for linear differential equations.”, BIT Numerical Mathematics, vol. 39, p. 281-304, 1999.
Lejeunes S., Modélisation de structures lamifiées élastomère-métal à l’aide d’une méthode de
réduction de modèles, PhD thesis, Université d’Aix-Mareille II, 2006.
Nedjar B., “ Frameworks for finite strain viscoelastic-plasticity based on multiplicative decomposition.
II: Computational aspects”, Computer Methods in Applied Mechanics and Engineering,
vol. 191, p. 1563-1593, 2002a.
Nedjar B., “ Frameworks for finite strain viscoelastic-plasticity based on multiplicative decomposition.
Part I: Continuum formulations”, Computer Methods in Applied Mechanics and
Engineering, vol. 191, p. 1541-1562, 2002b.
Reese S., Govindjee S., “ A theory of finite viscoelasticity and numerical aspects.”, International
Journal of Solid and Structures, vol. 35, p. 3455-3482, 1998.
Sidoroff F., “ The geometrical concept of intermediate configuration and elastic finite strain”,
Arch. Mech., vol. 25, n° 2, p. 299-309, 1973.
Sidoroff F., “ Variables internes en viscoélasticité, 2. Milieux avec configuration intermédiaire”,
J. Méc., vol. 14, n° 4, p. 571-595, 1975.
Sidoroff F., “ Variables internes en viscoélasticité, 3. Milieux avec plusieurs configurations
intermédiaires”, J. Méc., vol. 15, n° 1, p. 85-118, 1976.
Simo J.-C., “ A framework for Finite Strain Elastoplasticity Based on Maximum Plastic Dissipation
and the Multiplicative Decomposition: Part II. Computational Aspects.”, Computer
Methods in Applied Mechanics and Engineering, vol. 79, p. 1-31, 1988.
Simo J., Hugues T., Computational inelasticity, 2000.
Weber G., Arnand L., “ Finite deformation constitutive equations and a time integration procedure
for isotropic hyperelastic-viscoplastic solids.”, Computer Methods in Applied Mechanics
and Engineering, vol. 79, p. 173-202, 1990.
