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

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

doi:10.1093/qjmam/hbv017

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

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

Authors

A.V. Pichugin

Danila Prikazchikov d.prikazchikov@keele.ac.uk

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