In this paper we establish necessary and sufficient conditions for the strong-ellipticity of the equations governing an isotropic (compressible) nonlinerly elastic material at equilibrium. Our work extends results of Knowles and Sternberg  who obtained such conditions for both ordinary and strong ellipticity in the special case when the underlying deformations are plane.
Institute for Mathematics and Its Applications>IMA Preprints Series
Simpson, H.; Spector, S..
On Copositive Matrices and Strong Ellipticity for Isotropic Elastic Materials.
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