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Title: Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids
Authors: Pichugin, AV
Prikazchikov, DA
Keywords: Explicit conditions;Elastic stiffness tensor;Ellipticity;Orthorhombic incompressible;Isotropic solids
Issue Date: 2015
Publisher: Oxford University Press (OUP)
Citation: Quarterly Journal of Mechanics and Applied Mathematics, 69(1): pp. 67-81, (2015)
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 & Sternberg (Arch. Rat. Mech. Anal., 83, 53-90 (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 & Sternberg in terms of components of the incremental stiffness tensor. In addition, the resulting conditions are specialized to higher symmetry classes and compared with strong ellipticity conditions for plane strain, commonly used in the literature.
ISSN: 1464-3855
Appears in Collections:Dept of Mathematics Research Papers

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