The objective of this paper is to present a new framework to formulate thermoelastic constitutive relations for initially isotropic rubberlike materials undergoing finite deformations. The strain-energy function for incompressible materials is extended to include the effects of compressibility and temperature changes. The novelty of this framework is that only a few material functions and material parameters to be fitted with the experimental data are required, and these functions and parameters have clear physical meaning. In order to validate the proposed formulation, the Gent–Gent model for incompressible rubbers is chosen as an illustrative example. A new expression of the Helmholtz free energy of rubberlike materials, which takes into account the material compressibility and thermal effect, is then derived. In this generalized Gent–Gent model, only one material function and six material parameters are introduced. It is shown that the generalized Gent–Gent model can be used to predict the stress-strain behavior over the entire range of deformation. Even for incompressible materials, the strain-energy function in this paper is different from that given by Gent himself. The generalized Gent–Gent model can also adequately describe the thermal-mechanical coupling effect, in which thermoelastic inversion phenomena occur.

References

References
1.
Arruda
,
E. M.
, and
Boyce
,
M. C.
,
1993
, “
A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials
,”
J. Mech. Phys. Solids
,
41
(
2
), pp.
389
412
.10.1016/0022-5096(93)90013-6
2.
Wu
,
P. D.
, and
Van Der Giessen
,
E.
,
1992
, “
On Improved 3-D Non-Gaussian Network Models for Rubber Elasticity
,”
Mech. Res. Comm.
,
19
(
5
), pp.
427
433
.10.1016/0093-6413(92)90021-2
3.
Boyce
,
M. C.
, and
Arruda
,
E. M.
,
2000
, “
Constitutive Models of Rubber Elasticity: A Review
,”
Rubber Chem. Technol.
,
73
(
3
), pp.
504
523
.10.5254/1.3547602
4.
Gent
,
A. N.
,
1996
, “
A New Constitutive Relation for Rubber
,”
Rubber Chem. Technol.
,
69
(
1
), pp.
59
61
.10.5254/1.3538357
5.
Ogden
,
R. W.
,
1972
, “
Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids
,”
Proc. R. Soc. Lond. A
,
326
(
1597
), pp.
565
584
.10.1098/rspa.1972.0026
6.
Ogden
,
R. W.
,
1982
, “
Elastic Deformation of Rubberlike Solids
,”
Mechanics of Solids (The Rodney Hill 60th Anniversary Volume)
,
H. G.
Hopkins
and
M. J.
Sewell
eds.,
Pergamon Press
,
Oxford
, UK, pp.
499
537
.
7.
Gent
,
A. N.
, and
Thomas
,
A. G.
,
1958
, “
Forms for the Stored (Strain) Energy Function for Vulcanized Rubber
,”
J. Polym. Sci.
,
28
(
118
), pp.
625
628
.10.1002/pol.1958.1202811814
8.
Boyce
,
M. C.
,
1996
, “
Direct Comparison of the Gent and the Arruda–Boyce Constitutive Models of Rubber Elasticity
,”
Rubber Chem. Technol.
,
69
(
5
), pp.
781
785
.10.5254/1.3538401
9.
Pucci
,
E.
, and
Saccomandi
,
G.
,
2002
, “
A Note on the Gent Model for Rubber-Like Materials
,”
Rubber Chem. Technol.
,
75
(
5
), pp.
839
851
.10.5254/1.3547687
10.
Horgan
,
C. O.
, and
Saccomandi
,
G.
,
2002
, “
A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity
,”
J. Elasticity
,
68
(
1–3
), pp.
167
176
.10.1023/A:1026029111723
11.
Horgan
,
C. O.
, and
Saccomandi
,
G.
,
2003
, “
Finite Thermoelasticity With Limiting Chain Extensibility
,”
J. Mech. Phys. Solids
,
51
(
6
), pp.
1127
1146
.10.1016/S0022-5096(02)00144-8
12.
Horgan
,
C. O.
,
Ogden
,
R. W.
, and
Saccomandi
,
G.
,
2004
, “
A Theory of Stress Softening of Elastomers Based on Finite Chain Extensibility
,”
Proc. R. Soc. Lond. A
,
460
(
2046
), pp.
1737
1754
.10.1098/rspa.2003.1248
13.
Beda
,
T.
,
2007
, “
Modeling Hyperelastic Behavior of Rubber: A Novel Invariant-Based and a Review of Constitutive Models
,”
J. Polym. Sci. B Polym/Phys.
,
45
(
13
), pp.
1713
1732
.10.1002/polb.20928
14.
Beatty
,
M. F.
,
2008
, “
On Constitutive Models for Limited Elastic, Molecular Based Materials
,”
Math. Mech. Solids
,
13
(
5
), pp.
375
387
.10.1177/1081286507076405
15.
Price
,
C.
,
1976
, “
Thermodynamics of Rubber Elasticity
,”
Proc. R. Soc. Lond. A
,
351
(
1666
), pp.
331
350
.10.1098/rspa.1976.0145
16.
Ogden
,
R. W.
,
1972
, “
Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Compressible Rubberlike Solids
,”
Proc. R. Soc. Lond. A
,
328
(
1575
), pp.
567
583
.10.1098/rspa.1972.0096
17.
Bischoff
,
E. J.
,
Arruda
,
E. M.
, and
Grosh
,
K.
,
2001
, “
A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations
,”
Rubber Chem. Technol.
,
47
(
4
), pp.
541
559
.10.5254/1.3544956
18.
Ogden
,
R. W.
,
1976
, “
Volume Changes Associated With the Deformation of Rubberlike Solids
,”
J. Mech. Phys. Solids
,
24
(
6
), pp.
323
338
.10.1016/0022-5096(76)90007-7
19.
Chadwick
,
P.
,
1974
, “
Thermo-Mechanics of Rubberlike Materials
,”
Philos. Trans. R. Soc. A
,
276
(
1260
), pp.
371
403
.10.1098/rsta.1974.0026
20.
Chadwick
,
P.
, and
Creasy
,
C. F. M.
,
1984
, “
Modified Entropic Elasticity of Rubberlike Materials
,”
J. Mech. Phys. Solids
,
32
(
5
), pp.
337
357
.10.1016/0022-5096(84)90018-8
21.
Penn
,
R. W.
,
1970
, “
Volume Changes Accompanying the Extension of Rubber
,”
Trans. Soc. Rheol.
,
14
, pp.
509
517
.10.1122/1.549176
22.
Simo
,
J. C.
, and
Pister
,
K. S.
,
1984
, “
Remarks on Rate Constitutive Equations for Finite Deformation Problems: Computational Implications
,”
Comput. Meth. Appl. Mech. Eng.
,
46
(
2
), pp.
201
215
.10.1016/0045-7825(84)90062-8
23.
Treloar
,
L. R. G.
,
1944
, “
Stress-Strain Data for Vulcanized Rubber Under Various Types of Deformation
,”
Trans. Faraday Soc.
,
40
, pp.
59
70
.10.1039/tf9444000059
24.
Treloar
,
L. R. G.
,
1975
,
The Physics of Rubber Elasticity
,
3rd ed.
,
Oxford University Press
,
Oxford, UK
.
25.
Ahmadi
,
H. R.
,
Gough
,
J.
,
Muhr
,
A. H.
, and
Thomas
,
A. G.
,
1999
, “
Bi-Axial Experimental Techniques High-Lighting the Limitations of a Strain-Energy Description of Rubber
,”
Proceedings of First European Conference on Constitutive Models for Rubber, Constitutive Models for Rubber
, Vienna, Austria, September 9–10,
A.
Dorfmann
, and
A. H.
Muhr
, eds.,
Balkema
,
Rotterdam, The Netherlands
, pp.
65
71
.
26.
Nah
,
C.
,
Lee
,
G. B.
,
Lim
,
J. Y.
,
Kim
,
Y. H.
,
SenGupta
,
R.
, and
Gent
,
A. N.
,
2010
, “
Problems in Determining the Elastic Strain Energy Function for Rubber
,”
Int. J. Nonlin. Mech.
,
45
(
3
), pp.
232
235
.10.1016/j.ijnonlinmec.2009.11.004
27.
Han
,
W. H.
,
Horkay
,
F.
, and
McKenna
,
G. B.
,
1999
, “
Mechanical and Swelling Behaviors of Rubber: A Comparison of Some Molecular Models With Experiment
,”
Math. Mech. Solids
,
4
(
2
), pp.
139
167
.10.1177/108128659900400201
28.
Gent
,
A. N.
, and
Lindley
,
P. B.
,
1959
, “
Internal Rupture of Bonded Rubber Cylinders in Tension
,”
Proc. R. Soc. Lond. A
,
249
(
1257
), pp.
195
205
.10.1098/rspa.1959.0016
29.
Horgan
,
C. O.
, and
Polignone
,
D. A.
,
1995
, “
Cavitation in Nonlinearly Elastic Solids: A Review
,”
Appl. Mech. Rev.
,
48
(
8
), pp.
471
485
.10.1115/1.3005108
30.
James
,
H. M.
, and
Guth
,
E.
,
1943
, “
Theory of the Elastic Properties of Rubber
,”
J. Chem. Phys.
,
11
(
10
), pp.
455
481
.10.1063/1.1723785
31.
Erbe
,
H. H.
,
1974
, “
Thermoelastic Effects in Incompressible Isotropic Solids
,”
Mech. Res. Comm.
,
1
(
3
), pp.
137
142
.10.1016/0093-6413(74)90004-4
32.
Shen
,
M.
, and
Croucher
,
M.
,
1975
, “
Contribution of Internal Energy to the Elasticity of Rubberlike Materials
,”
J. Macromol. Sci.-Revs. Macromol. Chem.
, C
12
(
2
), pp.
287
329
.10.1080/15321797508076109
33.
Ogden
,
R. W.
,
1987
, “
Aspects of the Phenomenological Theory of Rubber Thermoelasticity
,”
Polymer.
,
28
(
3
), pp.
379
385
.10.1016/0032-3861(87)90189-3
34.
Ogden
,
R. W.
,
1992
, “
On the Thermoelastic Modeling of Rubberlike Solids
,”
J. Therm. Stresses
,
15
(
4
), pp.
533
557
.10.1080/01495739208946155
35.
Humphrey
,
J. D.
, and
Rajagopal
,
K. R.
,
1998
, “
Finite Thermoelasticity of Constrained Elastomers Subject to Biaxial Loading
,”
J. Elasticity
,
49
(
3
), pp.
189
200
.10.1023/A:1007472623454
36.
Holzapfel
,
G. A.
,
2000
,
Nonlinear Solid Mechanics, A Continuum Approach for Engineering
,
John Wiley and Sons
,
Chichester, UK
, pp.
305
356
.
37.
Huang
,
Z. P.
,
2012
,
Fundamentals of Continuum Mechanics, 2nd ed.
,
Higher Education Press
,
Beijing
, pp.
318
324
(in Chinese).
38.
Joule
,
J. P.
,
1859
, “
On Some Thermo-Dynamic Properties of Solids
,”
Phil Trans. R. Soc. Lond.
,
149
, pp.
91
131
.10.1098/rstl.1859.0005
39.
Wood
,
L. A.
, and
Martin
,
G. M.
,
1964
, “
Compressibility of Natural Rubber at Pressure Below 500 kg/cm2
,”
J. Res. Nat. Bur. Stand.
,
A 68
(
3
), pp.
259
268
.10.6028/jres.068A.022
You do not currently have access to this content.