The purpose of this research is to investigate the steady rotation of a solid cylinder for a class of strain-energy densities that are able to describe hardening phenomena in rubber. It is well known that use of the classic neo-Hookean strain energy gives rise to physically unrealistic response in this problem. In particular, solutions exist only for a sufficiently small angular velocity. As the velocity approaches this limiting value, the analysis predicts that the rotating cylinder collapses to a disk. It is shown here that this nonphysical behavior does not occur when generalized neo-Hookean models, which exhibit hardening at large deformations, are used.

1.
Mark, J. E., and Erman, B., 1988, Rubberlike Elasticity: A Molecular Primer, John Wiley and Sons, New York.
2.
Gent
,
A. N.
,
1996
, “
A New Constitutive Relation for Rubber
,”
Rubber Chem. Technol.
,
69
, pp.
59
61
.
3.
Boyce
,
M. C.
,
1996
, “
Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity
,”
Rubber Chem. Technol.
,
69
, pp.
781
785
.
4.
Horgan
,
C. O.
, and
Saccomandi
,
G.
,
1999
, “
Simple Torsion of Isotropic, Hyperelastic, Incompressible Materials With Limiting Chain Extensibility
,”
J. Elast.
,
56
, pp.
159
170
.
5.
Horgan
,
C. O.
, and
Saccomandi
,
G.
,
1999
, “
Pure Axial Shear of Isotropic Incompressible Nonlinearly Elastic Materials With Limiting Chain Extensibility
,”
J. Elast.
,
57
, pp.
307
319
.
6.
Horgan
,
C. O.
, and
Saccomandi
,
G.
,
2001
, “
Pure Azimuthal Shear of Isotropic Incompressible Hyperelastic Materials With Limiting Chain Extensibility
,”
Int. J. Non-Linear Mech.
,
36
, pp.
465
475
.
7.
Knowles
,
J. K.
,
1977
, “
The Finite Anti-Plane Shear Field Near the Tip of a Crack for a Class of Incompressible Elastic Solids
,”
Int. J. Fract.
,
13
, pp.
611
639
.
8.
Erman
,
B.
, and
Mark
,
J. E.
,
1988
, “
Use of Fixman-Alben Distribution Function in the Analysis of Non-Gaussian Rubber-Like Elasticity
,”
J. Chem. Phys.
,
89
, pp.
3314
3316
.
9.
Chadwick
,
P.
,
Creasy
,
C. F. M.
, and
Hart
,
V. G.
,
1977
, “
The Deformation of Rubber Cylinders and Tubes by Rotation
,”
J. Aust. Math. Soc. B, Appl. Math.
,
20
, Series 13, pp.
62
96
.
10.
Ogden, R. W., 1984, Non-linear Elastic Deformations, Ellis Horwood, Chichester, UK, reprinted by Dover, New York, 1997.
11.
Haughton
,
D. M.
, and
Ogden
,
R. W.
,
1980
, “
Bifurcation of Finitely Deformed Rotating Cylinders
,”
Q. J. Mech. Appl. Math.
,
33
, pp.
251
265
.
12.
Hunter, S. C., 1976, Mechanics of Continuous Media, Ellis Horwood, Chichester, UK.
13.
Mott
,
P. H.
, and
Roland
,
C. M.
,
1996
, “
Elasticity of Natural Rubber Networks
,”
Macromolecules
,
29
, pp.
6941
6945
.
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