Compression of Bonded Annular Rubber Blocks
Publication: Journal of Engineering Mechanics
Volume 121, Issue 6
Abstract
The load-deflection relation and stress distribution of bonded annular rubber blocks are first derived by an approximate-linear approach. The solution approaches the exact relation asymptotically as the block thickness reduces. A general formula for the nonlinear load-deflection relation is then presented, based on a variational method, in which no specific form of the strain-energy function is required. An explicit approximate analytical solution is obtained by applying the general formula to a neo-Hookean material. The approximate solutions are compared with the finite-element analysis. The relationships among the stiffness, the shape factor s, and the diameter ratio β are explored in detail and some interesting phenomena are observed. For example, a centrally placed tiny hole in a very thin circular disk can cause a sharp drop in its stiffness.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Beatty, M. F. (1977). “Elastic stability of rubber bodies in compression.”Finite elasticity, R. S. Rivlin, ed., Am. Soc. of Mech. Engrs., New York, N.Y.
2.
Benthem, J. P., and Minderhoud, P. (1972). “The problem of solid cylinder compressed between rough rigid stamps.”Int. J. of Solids and Struct., Vol. 8, 1027–1042.
3.
Chalhoub, M. S., and Kelly, J. M.(1990). “Effect of bulk compressibility on the stiffness of cylindrical base isolation bearing.”Int. J. of Solids and Struct., 26(7), 743–760.
4.
Chen, W. T., and Nelson, C. W.(1979). “Thermal stress in bonded joints.”IBM J. Res. Development, 23(2), 179–187.
5.
Fung, Y. C. (1965). Foundations of solid mechanics . Prentice-Hall, Inc., Englewood Cliffs, N.J.
6.
Gent, A. N., and Lindley, P. B.(1959). “The compression of bounded rubber blocks.”Proc., Instn. Mech. Engrs., London, England, 173(3), 111–117.
7.
Gent, A. N., and Meinecke, E. A.(1970). “Compression, bending and shear of bonded rubber blocks.”Polymer Engrg. Sci., 10(1), 48–73.
8.
Gent et al.(1974). “Interfacial stresses for bonded rubber blocks in compression and shear.”J. Appl. Mech., 41(4), 855–859.
9.
Green, A. E., and Zerna, W. (1968). Theoretical elasticity . Oxford University Press, Oxford, England.
10.
Holownia, B. P.(1971). “Compression of bonded rubber blocks.”J. Strain Anal., 6(2), 121–123.
11.
Lindley, P. B. (1966). Engineering design with natural rubber . Natural Rubber Producer's Res. Association, London, England.
12.
Ling, Y., Engle, P. A., and Brodsky, W. L.(1992). “Nonlinear load-deflection relations of bonded circular disks and infinite long strips.”Rubber Chem. and Technol., 65(5), 927–931.
13.
Ling, Y., Engel, P. A., and Geer, J. F.(1994). “The end problem of incompressible elastic cylinders.”J. Appl. Mech., 61(1), 30–37.
14.
Lukomskaya, A. I.(1965). “Equilibrium compression of rubber samples in practical tests.”Polymer Mech., 1(4), 46–49.
15.
Payne, A. R. (1959). “Shape factors and functions in rubber engineering.”The Engr., London, England, 207(Feb.), 328–333, 368–370.
16.
Rivlin, R. S. (1949). “Large elastic deformations of isotropic materials, part VI, further results in the theory of torsion, shear and flexure.”Phil. Trans., Royal Soc., London, England, A242, 173–195.
17.
Suhir, E.(1989). “Axisymmetric elastic deformation of a finite circular cylinder with application to low temperature strains and stresses in solder joints.”J. Appl. Mech., 56(2), 328–333.
18.
Swan, G. W.(1968). “The semi-infinite cylinder with prescribed end displacements.”SIAM J. Appl. Mathematics, 16(2), 860–881.
19.
Thornton, J. S.(1988). “Analysis of interfacial stresses for elastomeric disks in compression.”Polymer Engrg. and Sci., 28(10), 655–659.
20.
Trelaor, L. R. (1958). Physics of rubber elasticity, 2nd Ed., Clarendon Press, Oxford, England.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jun 1, 1995
Published in print: Jun 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.