We consider a conformal contact problem between a rubber band and rigid cylinders that involves geometrical and material nonlinearities. The rubber band is assumed to be incompressible, neo-Hookean rubber. From the geometry and elasticity of the band, we present simple formulas to estimate the force–stretch relations and the contact pressure distributions on the cylinder. We show that the theoretical results are in good agreement with those of the finite element analysis when the rubber band is thin enough to be negligible to the bending stiffness. This verifies that the theory can effectively take into account both the material and geometrical nonlinearities of the band under the present conditions.

References

References
1.
Gent
,
A. N.
, 2001,
Engineering With Rubber: How to Design Rubber Components
,
Hanser Gardner Publications
,
Cincinnati, OH
.
2.
Kelly
,
J. M.
, 1997,
Earthquake-resistant Design with Rubber
,
2nd ed.
,
Springer
,
Berlin
.
3.
Gent
,
A. N.
, and
Lindley
,
P. B.
, 1959, “
The Compression of Bonded Rubber Blocks
,”
Proc. Inst. Mech. Eng.
,
173
, pp.
111
222
.
4.
Charrier
,
J. M.
, and
Gent.
A. N.
, 1970, “
Inflation and Compression of Rubber Tubes Between Parallel Plates
,”
Polym. Eng. Sci.
,
10
, pp.
358
363
.
5.
Ibrahim
,
R. A.
, 2008, “
Recent Advances in Nonlinear Passive Vibration Isolators
,”
J. Sound Vib.
,
314
, pp.
371
452
.
6.
Shangguan
,
W.-B.
, 2009, “
Engine Mounts and Powertrain Mounting Systems: A Review
,”
Int. J. Veh. Des.
,
49
, pp.
237
258
.
7.
Kluppel
,
M.
, and
Heinrich
,
G.
, 2000, “
Rubber Friction on Self-Affine Road Tracks
,”
Rubber Chem. Tech.
,
73
, pp.
578
606
.
8.
Persson
,
B. N. J.
, 2001, “
Theory of Rubber Friction and Contact Mechanics
,”
J. Chem. Phys.
,
115
, pp.
3840
3861
.
9.
Persson
,
B. N. J.
,
Albohr
,
O.
,
Tartagino
,
U.
,
Volokitin
,
A. I.
, and
Tosatti
,
E.
, 2005, “
On the Nature of Surface Roughness With Application to Contact Mechanics, Sealing, Rubber Friction and Adhesion
,”
J. Phys. Condens. Matter
,
17
, pp.
R1
R62
.
10.
Euler
,
L.
1762, “
Remarques Sur L’effect du Frottement Dans L’equilibre
,”
Mém. Acad. Sci.
,
18
, pp.
265
278
.
11.
Treloar
,
L. R. G.
, 1975,
The Physics of Rubber Elasticity
,
3rd ed.
,
Oxford University Press
,
New York
.
12.
Reynolds
,
O.
, 1874, “
On the Efficiency of Belts or Straps as Communicators of Work
,”
Engineer (London)
,
38
, p.
396
.
13.
Rubin
,
M. B.
, 2000, “
An Exact Solution for Steady Motion of an Extensible Belt in Multipulley Belt Drive Systems
,”
ASME J. Mech. Des.
,
122
, pp.
311
316
.
You do not currently have access to this content.