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Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids.

Pichugin, A.V.; Prikazchikov, D.A.

Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids. Thumbnail


Authors

A.V. Pichugin



Abstract

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee and Sternberg (Arch. Rat. Mech. Anal. 83 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stressed incompressible isotropic solids. This allows us to reformulate the results by Zee and Sternberg in terms of components of the incremental stiffness tensor. In addition, the resulting conditions are specialised to higher symmetry classes and compared with strong ellipticity conditions for plane strain, commonly used in the literature.

Journal Article Type Article
Acceptance Date Nov 4, 2015
Online Publication Date Nov 30, 2015
Publication Date 2016-02
Journal Quarterly Journal of Mechanics and Applied Mathematics
Print ISSN 0033-5614
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 69
Issue 1
Pages 67-81
DOI https://doi.org/10.1093/qjmam/hbv017
Publisher URL https://doi.org/10.1093/qjmam/hbv017

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