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The Quarterly Journal of Mechanics and Applied Mathematics 1991 44(2):241-248; doi:10.1093/qjmam/44.2.241
© 1991 by Oxford University Press
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A NOTE ON A GENERALIZED SHEAR DEFORMATION

M. ARON

( Department of Mathematics and Statistics, Polytechnic South West Drake Circus, Plymouth PL4 8AA )

In the absence of body forces a certain generalized shear deformation is shown to be possible in an unconstrained isotropic elastic solid if and only if the elastic solid satisfies a condition which renders it incapable of obeying the Baker-Ericksen (BE) inequalities. In the case when the elastic solid satisfies the weakened BE inequalities the deformation (which must necessarily occur at constant pressure on the boundary of the body and null Cauchy deviatoric stress) is shown to be at best neutrally stable. Thus, for this particular deformation, we are able to confirm Ericksen's conjecture regarding the stability of Varley-Day solutions to the equations of elastostatics.


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