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Surface instabilities on an equibiaxially stretched elastic half-space

Published online by Cambridge University Press:  24 October 2008

B. D. Reddy
B. D. Reddy
Affiliation:
University of Cape Town
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Extract

The existence of non-homogeneous modes of deformation in an equibiaxially stretched elastic half-space is investigated. The surface of the half-space is assumed to be traction-free.

It is shown that three different eigenmodal deformations are possible, according as the cube of the critical stretch is greater than, less than, or equal to ¾.

For the class of strain-energy functions due to Ogden (9), necessary conditions for bifurcation are deduced-for equibiaxial tension. Results are given and discussed for single-term, as well as two- and three-term Ogden strain-energy functions, for equibiaxial tension and compression.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 491 - 501
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Green, A. E. and Zerna, W.Theoretical elasticity, 2nd ed. (Oxford University Press, 1965).Google Scholar
(2)Nowinski, J. L.Surface instability of a half-space under high two-dimensional compression. J. Franklin Inst. 288, (1969), 367–376.Google Scholar
(3)Biot, M. A.Mechanics of incremental deformations (Wiley, New York, 1965).Google Scholar
(4)Sawyers, K. N. Material stability and bifurcation in finite elasticity. In Finite elasticity, AMD, vol. 27, ed. Rivlin, R. S. (Asme, New York, 1977).Google Scholar
(5)Hill, R. and Hutchinson, J. W.Bifurcation phenomena in the plane tension test. J. Mech. Phys. Solids 23 (1975), 239–264.CrossRefGoogle Scholar
(6)Young, N. J. B.Bifurcation phenomena in the plane compression test. J. Mech. Phys. Solids 24 (1976), 77–91.CrossRefGoogle Scholar
(7)Bassani, J. L., Durban, D. and Hutchinson, J. W.Bifurcation at a spherical hole in an infinite elastoplastic medium. Proc. Cambridge Philos. Soc. 87 (1980), 339–356.CrossRefGoogle Scholar
(8)Hutchinson, J. W. and Tvergaard, V.Surface instabilities on statically strained plastic solids. Int. J. Mech. Sci. 22 (1980), 339–354.Google Scholar
(9)Ogden, R. W.Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. London, Ser. A 326 (1972), 565–584.Google Scholar
(10)Ogden, R. W.On stress rates in solid mechanics with application to elasticity theory. Proc. Cambridge Philos. Soc. 75 (1974), 303–319.Google Scholar
(11)Haughton, D. M. and Ogden, R. W.On the incremental equations in non-linear elasticity II. Bifurcation of pressurised spherical shells. J. Mech. Phys. Solids 26 (1978), 111–138.CrossRefGoogle Scholar