In this paper we establish necessary and sufficient conditions, in terms of the local principal stretches, for ordinary and strong ellipticity of the equations governing finite plane equilibrium deformations of a compressible hyperelastic solid. The material under consideration is assumed to be homogeneous and isotropic, but its strain-energy density is otherwise unrestricted. We also determine the directions of the characteristic curves appropriate to plane elastostatic deformations that are accompanied by a failure of ellipticity.
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The results communicated in this paper were obtained in the course of an investigation supported by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.
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Knowles, J.K., Sternberg, E. On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch. Rational Mech. Anal. 63, 321–336 (1976). https://doi.org/10.1007/BF00279991
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