Abstract
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 parameterf occurring in the generalized Blatz-Ko model is in the range 0≤f<1, it is shown that ellipticity is always lost at sufficiently large stretches, while forf=1, the equilibrium equations are globally elliptic. The implications of these results for a variety of physical problems are discussed.
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Horgan, C.O. Remarks on ellipticity for the generalized Blatz-Ko constitutive model for a compressible nonlinearly elastic solid. J Elasticity 42, 165–176 (1996). https://doi.org/10.1007/BF00040959
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DOI: https://doi.org/10.1007/BF00040959