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On the ellipticity of the equations of nonlinear elastostatics for a special material

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Summary

This paper deals with the ellipticity of the equations of finite elastostatics for a compressible material that corresponds to a special choice of the strain-energy density and has received repeated attention in the literature. The possible failure of ellipticity of the appropriate system of displacement equations of equilibrium at solutions involving large deformations was suggested by certain difficulties encountered in an attempt to determine the deformations and stresses arising in such a material near the tip of a crack. It is shown here that ellipticity prevails only if the principal stretches are suitably restricted and breaks down, in particular, at a local state of uni-axial tension or compression of sufficiently severe intensity.

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References

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Authors and Affiliations

  1. California Institute of Technology, 91125, Pasadena, California, USA

    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 ellipticity of the equations of nonlinear elastostatics for a special material. J Elasticity 5, 341–361 (1975). https://doi.org/10.1007/BF00126996

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  • DOI: https://doi.org/10.1007/BF00126996

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