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Remarks on ellipticity for the generalized Blatz-Ko constitutive model for a compressible nonlinearly elastic solid. (English) Zbl 0852.73019
Summary: One of the most widely used constitutive models for compressible isotropic nonlinearly elastic solids is the generalized Blatz-Ko material for foam-rubber and its various specializations. For this model, a unified derivation of necessary and sufficient conditions for ellipticity of the governing three-dimensional displacement equations of equilibrium is provided. When the parameter \(f\) occurring in the generalized Blatz-Ko model is in the range \(0\leq f<1\), it is shown that ellipticity is always lost at sufficiently large stretches, while for \(f=1\), the equilibrium equations are globally elliptic. The implications of these results for a variety of physical problems are discussed.

74B20 Nonlinear elasticity
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