Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem |
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Authors: | D Y Gao R W Ogden |
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Institution: | (1) Department of Mathematics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA;(2) Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK |
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Abstract: | The pure azimuthal shear problem for a circular cylindrical tube of nonlinearly elastic material, both isotropic and anisotropic,
is examined on the basis of a complementary energy principle. For particular choices of strain-energy function, one convex
and one non-convex, closed-form solutions are obtained for this mixed boundary-value problem, for which the governing differential
equation can be converted into an algebraic equation. The results for the non-convex strain energy function provide an illustration
of a situation in which smooth analytic solutions of a nonlinear boundary-value problem are not global minimizers of the energy
in the variational statement of the problem. Both the global minimizer and the local extrema are identified and the results
are illustrated for particular values of the material parameters.
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Keywords: | 74B20 74P99 |
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