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

Prikazchikov

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.

• Acceptance Date: Nov 4, 2015
• Publication Date: Nov 30, 2015
• Journal: Quarterly Journal of Mechanics and Applied Mathematics
• Print ISSN: 0033-5614
• Publisher: Oxford University Press
• Pages: 67-81
• DOI: https://doi.org/10.1093/qjmam/hbv017
• Publisher URL: https://doi.org/10.1093/qjmam/hbv017