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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(1):105-122; doi:10.1093/qjmam/56.1.105
© 2003 by Oxford University Press
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On Helical Shear of a Compressible Elastic Circular Cylindrical Tube

E. Kirkinis1 and R. W. Ogden1

( 1 Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW )

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

Received 19 February 2002. Revised 29 May 2002.


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