We present a phenomenological three-dimensional (3D) nonlinear viscoelastic constitutive model for time-dependent analysis. Based on Schapery's single integral constitutive law, a solution procedure has been provided to solve nonlinear viscoelastic behavior. This procedure is applicable to 3D problems and uses time- and stress-dependent material properties to characterize the nonlinear behavior of material. The equations describing material behavior are chosen based on the measured material properties in a short test time frame. This estimation process uses the Prony series material parameters, and the constitutive relations are based on the nonseparable form of equations. Material properties are then modified to include the long-term response of material. The presented model is suitable for the development of a unified computer code that can handle both linear and nonlinear viscoelastic material behavior. The proposed viscoelastic model is implemented in a user-defined material algorithm in abaqus (UMAT), and the model validity is assessed by comparison with experimental observations on polyethylene for three uniaxial loading cases, namely short-term loading, long-term loading, and step loading. A part of the experimental results have been conducted by (Liu, 2007, “Material Modelling for Structural Analysis of Polyethylene,” M.Sc. thesis, University of Waterloo, Waterloo, ON Canada), while the rest are provided by an industrial partner. The research shows that the proposed finite element model can reproduce the experimental strain–time curves accurately and concludes that with proper material properties to reflect the deformation involved in the mechanical tests, the deformation behavior observed experimentally can be accurately predicted using the finite element simulation.

References

References
1.
Xia
,
Z.
,
Shen
,
X.
, and
Ellyin
,
F.
,
2006
, “
An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule
,”
Mech. Time-Dependent Mater.
,
9
(
4
), pp.
281
300
.
2.
Flugge
,
W.
,
1967
,
Viscoelasticity
,
Blaisdell Publishing Company
, Waltham, MA.
3.
Schapery
,
R. A.
,
1969
, “
On the Characterization of Nonlinear Viscoelastic Materials
,”
Polym. Eng. Sci.
,
9
(
4
), pp.
295
310
.
4.
Lustig
,
S. R.
, and
Shay
,
R. M.
,
1996
, “
Thermodynamics Constitutive Equations for Materials With Memory on a Material Time Scale
,”
J. Rheol.
,
40
(
1
), pp.
69
106
.
5.
Weitsman
,
Y.
,
1990
, “
A Continuum Diffusion Model for Viscoelastic Materials
,”
J. Phys. Chem.
,
94
(
2
), pp.
961
968
.
6.
Mlekusch
,
B.
,
2001
, “
Calculation of Residual Stress Development in Injection Moulding Using a Nonlinear Viscoelastic Model
,”
Mech. Time-Depend. Mat.
,
5
(
2
), pp.
101
118
.
7.
Popelar
,
C. F.
, and
Liechi
,
K. M.
,
2003
, “
A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior
,”
Mech. Time-Depend. Mat.
,
7
(
2
), pp.
89
141
.
8.
Green
,
A. E.
, and
Rivlin
,
R. S.
,
1957
, “
The Mechanics of Non-Linear Materials With Memory
,”
Arch. Rational Mech. Anal.
,
1
(
1
), pp.
1
21
.
9.
Lockett
,
F. J.
,
1972
,
Nonlinear Viscoelastic Solids
,
Academic Press
,
New York
.
10.
Schapery
,
R. A.
,
1969
, Further Development of a Thermodynamic Constitutive Theory: Stress Formulation, Purdue University, Purdue Research Foundation, Lafayette, IN.
11.
Hiel
,
C.
,
Cardon
,
A. H.
, and
Brinson
,
H. F.
,
1983
, “
The Nonlinear Viscoelastic Response of Resin Matrix Composite Laminates
,”
Composite Structures
, Virginia Polytechnic Institute and State University,
Blacksburg, VA
.
12.
Findley
,
W. N.
,
Lai
,
J. S.
, and
Onaran
,
K.
,
1976
,
Creep and Relaxation of Nonlinear Viscoelastic Materials
, Vol.
18
,
North-Holland Publishing
, Amsterdam, The Netherlands.
13.
Sepiani
,
H.
,
Polak
,
M. A.
, and
Penlidis
,
A.
,
2017
, “
Modeling Short- and Long-Term Time-Dependent Nonlinear Behaviour of Polyethylene
,”
Mech. Adv. Mater. Struct.
,
25
(
7
), pp.
600
610
.
14.
Roy
,
S.
, and
Reddy
,
J. N.
,
1988
, “
A Finite Element Analysis of Adhesively Bonded Composite Joints With Moisture Diffusion and Delayed Failure
,”
Comput. Struct.
,
29
(
6
), pp.
1011
1031
.
15.
Williams
,
M. L.
,
Landel
,
R. F.
, and
Ferry
,
J. D.
,
1955
, “
The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass Forming Liquids
,”
J. Am. Chem. Soc.
,
77
(
14
), pp.
3701
3707
.
16.
Ferry
,
J. D.
,
1980
,
Viscoelastic Properties of Polymers
,
Wiley
,
New York
.
17.
Liu
,
H.
,
2007
, “
Material Modelling for Structural Analysis of Polyethylene
,”
M.Sc. thesis
, University of Waterloo, Waterloo, ON, Canada.https://uwspace.uwaterloo.ca/bitstream/handle/10012/2646/Thesis_HongtaoLIU_CivilEng.pdf?sequence=
18.
Krishnaswamy
,
P.
,
Tuttle
,
M. E.
, and
Emery
,
A. F.
,
1992
, “
Finite Element Modeling of the Time-Dependent Behavior of Nonlinear Ductile Polymers
,”
Polym. Eng. Sci.
,
32
(
16
), pp.
1086
1096
.
19.
Hinterhoelzl
,
R. M.
, and
Schapery
,
R. A.
,
2004
, “
FEM Implementation of a Three-Dimensional Viscoelastic Constitutive Model for Particulate Composites With Damage Growth
,”
Mech. Time-Depend. Mater.
,
8
(
1
), pp.
65
94
.
20.
MacCallum
,
R. C.
,
Browne
,
M. W.
, and
Sugawara
,
H. M.
,
1996
, “
Power Analysis and Determination of Sample Size for Covariance Structure Modeling
,”
Psychol. Methods
,
1
(
2
), pp.
130
149
.
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