In this paper we present a theory of finite deformation viscoelasticity. The presentation is not restricted to small perturbations from the elastic equilibrium in contrast to many viscoelasticity theories. The fundamental hypothesis of our model is the multiplicative viscoelastic decomposition of Sidoroff (1974). This hypothesis is combined with the assumption of a viscoelastic potential to give a model that is formally similar to finite associative elasto-plasticity. Examples are given to compare the present proposal to an alternative formulation in the literature for the cases of uniaxial plane strain relaxation and creep.
Issue Section:
Technical Papers
1.
Bernstein
B.
Kearsley
E. A.
Zapas
L. J.
1967
, “A Study of Stress Relaxation with Finite Strain
,” Trans. Soc. Rheo.
Vol. 7
, pp. 391
–410
.2.
Eterovic
A. L.
Bathe
K. J.
1990
, “A Hyperelastic-Based Large Strain Elasto-Plastic Constitutive Formulation with Combined Isotropic-Kinematic Hardening Using the Logarithmic Stress and Strain Measures
,” Int. J. Numer. Meth. Engng.
, Vol. 30
, pp. 1099
–1114
.3.
Govindjee
S.
Simo
J. C.
1993
, “Coupled Stress-Diffusion: Case II
,” J. Mech. Phys. Solids
, Vol. 41
, pp. 863
–887
.4.
Govindjee
S.
Simo
J. C.
1992
, “Mullins’ Effect and the Strain Amplitude Dependence of the Storage Modulus
,” Int. J. Solids Structures
, Vol. 29
, pp. 1737
–1751
.5.
Gurtin, M. E., 1981, An Introduction to Continuum Mechanics, Academic Press, New York.
6.
Herrmann, L. R. and Peterson, F. E., 1968, “A Numerical Procedure for Visco-Elastic Stress Analysis,” Proc. 7th Meeting of ICRPG Mechanical Behavior Working Group, Orlando, FL.
7.
Knauss
W.
Emri
I.
1981
, “Non-Linear Viscoelasticity Based on Free Volume Consideration
,” Computers & Structures
, Vol. 13
, pp. 123
–128
.8.
Le Tallec
P.
Rahier
C.
1994
, “Numerical Models of Steady Rolling for Non-Linear Viscoelastic Structures in Finite Deformations
,” Int. J. Numer. Meth. Engng.
, Vol. 37
, pp. 1159
–1186
.9.
Le Tallec
P.
Rahier
C.
Kaiss
A.
1993
, “Three-Dimensional Incompressible Viscoelasticity in Large Strains: Formulation and Numerical Approximation
,” Comp. Meth. Appl. Mech. Engng.
, Vol. 109
, pp. 233
–258
.10.
Lion, A., 1996, “On the Mathematical Representation of the Thermomechanical Behaviour of Elastomers” Institute of Mechanics, Univ. of Kassel Report: 1/1996.
11.
Lubliner
J.
1985
, “A model of rubber viscoelasticity
,” Mech. Res. Comm.
, Vol. 12
, pp. 93
–99
.12.
Miehe
C.
1994
, “Aspects of the Formulation and Finite Element Implementation of Large Strain Isotropic Elasticity
,” International Journal of Numerical Methods in Engineering
, Vol. 37
, pp. 1981
–2004
.13.
Poincare´, H., 1929, The Foundations of Science, Translation: B. Halstep, The Science Press.
14.
Reese, S., and Govindjee, S., 1996, “A Theory of Finite Viscoelasticity and Numerical Aspects,” UC Berkeley Report: UCB/SEMM-96/08, (submitted to Int. J. Solids Structures).
15.
Sidoroff
F.
1974
, “Un mode`le viscoe´lastique non line´aire avec configuration interme´diaire
,” J. de Me´canique
, Vol. 13
, pp. 679
–713
.16.
Simo
J. C.
1987
, “On a Fully Three-Dimensional Finite-Strain Viscoelastic Damage Model: Formulation and Computational Aspects
,” Comp. Meth. Appl. Mech. Engng.
, Vol. 60
, pp. 153
–173
.17.
Simo
J. C.
1992
, “Algorithms for Static and Dynamic Multiplicative Plasticity That Preserve the Classical Return Mapping Schemes of the Infinitesimal Theory
,” Computer Methods in Applied Mechanics and Engineering
Vol. 99
, pp. 61
–112
.18.
Simo
J. C.
Miehe
C.
1992
, “Associative coupled thermoplasticity at finite strains
,” Computer Methods in Applied Mechanics and Engineering
, Vol. 98
, pp. 41
–104
.19.
Taylor
R. L.
Pister
K. S.
Goudreau
G. L.
1970
, “Thermomechanical Analysis of Viscoelastic Solids
,” Int. J. Numer. Meth. Engng.
, Vol. 2
, pp. 45
–59
.20.
Weber
G.
Anand
L.
1990
, “Finite Deformation. Constitutive Equations and a Time Integration Procedure for Isotropic Hyperelastic-Viscoplastic Solids
,” Computer Methods in Applied Mechanics and Engineering
, Vol. 79
, pp. 173
–202
.
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