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

Knowles, J. K. and Sternberg, Eli (1975) On the ellipticity of the equations of nonlinear elastostatics for a special material. Journal of Elasticity, 5 (3-4). pp. 341-361. ISSN 0374-3535. http://resolver.caltech.edu/CaltechAUTHORS:20151109-145649593

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF00126996DOIArticle
http://link.springer.com/article/10.1007%2FBF00126996PublisherArticle
Additional Information:© 1975 Noordhoff International Publishing-Leyden. Received May 14, 1975. 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
Record Number:CaltechAUTHORS:20151109-145649593
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20151109-145649593
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62007
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Nov 2015 23:13
Last Modified:09 Nov 2015 23:13

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