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

Knowles, J. K. and Sternberg, Eli (1976) On the failure of ellipticity of the equations for finite elastostatic plane strain. Archive for Rational Mechanics and Analysis, 63 (4). pp. 321-336. ISSN 0003-9527. doi:10.1007/BF00279991.

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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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Additional Information:© 1976 Springer. Received June 29, 1976. 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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Office of Naval Research (ONR)N00014-75-C-0196
Issue or Number:4
Record Number:CaltechAUTHORS:20151124-104106498
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62368
Deposited By: Tony Diaz
Deposited On:24 Nov 2015 19:08
Last Modified:10 Nov 2021 23:01

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