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A note on anti-plane shear for compressible materials in finite elastostatics

Published online by Cambridge University Press:  17 February 2009

James K. Knowles
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, United States of America
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Abstract

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This note gives a necessary and sufficient condition that a compressible, isotropic elastic material should admit non-trivial states of finite anti-plane shear.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Adkins, J. E., “Some generalizations of the shear problem for isotropic incompressible materials”, Proc. Cambridge Philos. Soc. 50 (1954), 334.CrossRefGoogle Scholar
[2]Blatz, P. J. and Ko, W. L., “Application of finite elastic theory to the deformation of rubbery materials”, Trans. Soc. Rheology 6 (1962), 223.CrossRefGoogle Scholar
[3]Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol 2, Interscience, New York (1962).Google Scholar
[4]Green, A. E. and Adkins, J. E., Large Elastic Deformations, Clarendon Press, Oxford (1960).Google Scholar
[5]John, F., “Plane elastic waves of finite amplitude. Hadamard materials and harmonic materials”, Communications on Pure and Applied Mathematics 19 (1966), 309.CrossRefGoogle Scholar
[6]Knowles, J. K., “On finite anti-plane shear for incompressible elastic materials”, J. Aust. Math. Soc. Series B Vol. 21 Part 4, (1976).Google Scholar
[7]Truesdell, C. and Noll, W., “The nonlinear field theories of mechanics”, Handbuch der Physik, Vol. 3/1, Springer, Berlin (1965).Google Scholar
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