Material Instabilities for Large Deformations of the Generalized Blatz-Ko Material

[+] Author and Article Information
C. O. Horgan

School of Engineering and Applied Science, University of Virginia, Charlottesville VA 22903

Appl. Mech. Rev 50(11S), S93-S96 (Nov 01, 1997) doi:10.1115/1.3101856 History: Online April 20, 2009


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.

Copyright © 1997 by American Society of Mechanical Engineers
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