In this paper, we study the combined torsion, circular and axial shearing of a compressible hyperelastic and prestressed tube. The analysis is carried out for a class of Ogden elastic material and the governing nonlinear equations are solved numerically using the Runge-Kutta method. The results reported present the effects of the torsion for different shearing loads on the local volume change and the circumferential stretch ratio. The effect of the second invariant-dependent behavior of polynomial materials is also investigated. [S0021-8936(00)01301-5]

1.
Ogden
,
R. W.
,
Chadwick
,
P.
, and
Haddon
,
E. W.
,
1973
, “
Combined Axial and Torsional Shear of Tube of Incompressible Isotropic Elastic Material
,”
Q. J. Mech. Appl. Math.
,
26
, pp.
23
41
.
2.
Mioduchowski
,
A.
, and
Haddow
,
J. B.
,
1979
, “
Combined Torsional and Axial Shear of a Compressible Hyperelastic Tube
,”
ASME J. Appl. Mech.
,
46
, pp.
223
226
.
3.
Levinson
,
M.
, and
Burgess
,
I. W.
,
1971
, “
A Comparison of Some Simple Constitutive Relations for Slightly Compressible Rubber-Like Materials
,”
Int. J. Mech. Sci.
,
13
, pp.
563
572
.
4.
Blatz
,
P. J.
, and
Ko
,
W. L.
,
1962
, “
Application of Finite Elastic Theory to the Deformation of Rubbery Materials
,”
Trans. Soc. Rheol.
,
6
, pp.
223
251
.
5.
Ogden
,
R. W.
, and
Isherwood
,
D. A.
,
1978
, “
Solution of Some Finite Plane-Strain Problems for Compressible Elastic Solids
,”
Q. J. Mech. Appl. Math.
,
31
, pp.
219
249
.
6.
Carroll
,
M. M.
, and
Horgan
,
C. O.
,
1990
, “
Finite Strain Solutions for a Compressible Elastic Solid
,”
Q. Appl. Math.
,
48
, No.
4
, pp.
767
780
.
7.
Tao
,
L.
,
Rajagopal
,
K. R.
, and
Wineman
,
A. S.
,
1992
, “
Circular Shearing and Torsion of Generalized Neo-Hookean Materials
,”
IMA J. Appl. Math.
,
48
, pp.
23
37
.
8.
Knowles
,
J. K.
, and
Sternberg
,
E.
,
1975
, “
On the Ellipticity of the Equations of Nonlinear Elastostatics for a Special Material
,”
J. Elast.
,
5
, pp.
341
361
.
9.
Abeyaratne
,
R.
, and
Knowles
,
J. K.
,
1987
, “
Non-elliptic Elastic Materials and the Modeling of Dissipative Mechanical Behavior: An Example
,”
J. Elast.
,
18
, pp.
227
278
.
10.
Horgan
,
C. O.
,
1996
, “
Remarks on Ellipticity for the Generalized Blatz-Ko Constitutive Model for Compressible Nonlinearly Elastic Solid
,”
J. Elast.
,
42
, pp.
165
176
.
11.
Zidi
,
M.
,
1999
, “
Torsion and Axial Shearing of a Compressible Hyperelastic Tube
,”
Mech. Res. Commun.
,
26
, No.
2
, pp.
245
252
.
12.
Zidi
,
M.
,
2000
, “
Circular Shearing and Torsion of a Compressible Hyperelastic and Prestressed Tube
,”
Int. J. Non-Linear Mech.
,
35
, pp.
201
209
.
13.
Sensening
,
C. B.
,
1965
, “
Non Linear Theory for the Deformation of Pre-stressed Circular Plates and Rings
,”
Commun. Pure Appl. Math.
,
18
, pp.
147
161
.
14.
Le Tallec
,
P.
, and
Vidrascu
,
M.
,
1984
, “
A Numerical Method for Solving Equilibrium Problems of Compressible Hyperelastic Bodies in Large Deformations
,”
Numer. Math.
,
43
, pp.
199
224
.
15.
Wineman
,
A. S.
, and
Waldron
, Jr.,
W. K.
,
1995
, “
Normal Stress Effects Induced During Circular Shear of a Compressible Non-linear Elastic Cylinder
,”
Int. J. Non-Linear Mech.
,
30
, No.
3
, pp.
323
339
.
16.
Ertepinar
,
A.
,
1990
, “
On the Finite Circumferential Shearing of Compressible Hyperelastic Tubes
,”
Int. J. Eng. Sci.
,
18
, No.
9
, pp.
889
896
.
17.
Beatty
,
M. F.
,
1987
, “
Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers and Biological Tissues—With Examples
,”
Appl. Mech. Rev.
,
40
, pp.
1699
1734
.
18.
Polignone
,
D. A.
, and
Horgan
,
C. O.
,
1991
, “
Pure Torsion of Compressible Nonlinearly Elastic Circular Cylinders
,”
Q. Appl. Math.
,
49
, No.
3
, pp.
591
607
.
19.
Polignone
,
D. A.
, and
Horgan
,
C. O.
,
1992
, “
Axisymmetric Finite Anti-plane Shear of Compressible Nonlinearly Elastic Circular Tubes
,”
Q. Appl. Math.
,
50
, pp.
323
341
.
20.
Haughton
,
D. M.
,
1993
, “
Shearing of Compressible Elastic Cylinders
,”
Q. J. Mech. Appl. Math.
,
46
, pp.
471
486
.
21.
Polignone
,
D. A.
, and
Horgan
,
C. O.
,
1994
, “
Pure Circular Shear of Compressible Non-linearly Elastic Tubes
,”
Q. Appl. Math.
,
50
, pp.
113
131
.
22.
Simmonds
,
J. G.
, and
Warne
,
P.
,
1992
, “
Azimuthal Shear of Compressible or Incompressible, Non-linearly Elastic Polar Orthotropic Tubes of Infinite Extent
,”
Int. J. Non-Linear Mech.
,
27
, No.
3
, pp.
447
464
.
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