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 discussion 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 ≤ 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 material instabilities in a variety of physical problems are discussed.

This content is only available via PDF.
You do not currently have access to this content.