Pichugin, AV and Prikazchikov, D (2015) Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids. Quarterly Journal of Mechanics and Applied Mathematics, 69 (1). pp. 67-81. ISSN 1464-3855

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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.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 21 Dec 2015 09:26
Last Modified: 18 Apr 2019 13:10
URI: https://eprints.keele.ac.uk/id/eprint/1325

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