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On the failure of ellipticity of the equations for finite elastostatic plane strain

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Summary

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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References

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Authors and Affiliations

  1. California Institute of Technology, Pasadena

    J. K. Knowles & Eli Sternberg

Authors
  1. J. K. Knowles
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  2. Eli Sternberg
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Additional information

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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  • DOI: https://doi.org/10.1007/BF00279991

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