On axisymmetric solutions for compressible nonlinearly elastic solids

1995 ◽  
pp. 107-125 ◽  
Author(s):  
Cornelius O. Horgan
Keyword(s):  
Elastic Solids ◽  
Axisymmetric Solutions ◽  
Nonlinearly Elastic

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

1997 ◽  
Vol 50 (11S) ◽  
pp. S93-S96 ◽  
Author(s):  
C. O. Horgan
Keyword(s):  
Large Deformations ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Constitutive Models ◽  
Equilibrium Equations ◽  
Elastic Solids ◽  
Foam Rubber ◽  
Physical Problems ◽  
Necessary And Sufficient ◽  
Nonlinearly Elastic

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.

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