scholarly journals Transverse waves in nonlinearly elastic solids and the Milne—Pinney (or Ermakov) equation

2011 ◽  
Vol 16 (6) ◽  
pp. 586-593 ◽  
Author(s):  
Michel Destrade ◽  
Giuseppe Saccomandi
Keyword(s):  
Elastic Solids ◽  
Transverse Waves ◽  
Nonlinearly Elastic

Identification of the Model of Nonlinear Elasticity in Dynamic Experiments

2021 ◽  
pp. 2150025
Author(s):  
Marina Sokolova ◽  
Yuri Astapov ◽  
Dmitrii Khristich
Keyword(s):  
Deformable Body ◽  
Polyamide 6 ◽  
Preliminary Deformation ◽  
Transverse Waves ◽  
Wave Velocities ◽  
Phase Velocities ◽  
Dynamic Methods ◽  
Dynamic Experiments ◽  
Effective Phase ◽  
Nonlinearly Elastic

Dynamic methods for identifying a model of a nonlinearly elastic deformable body are considered. By the effective phase velocities of longitudinal and transverse waves propagating along and across the axis of the compressed bar, it is possible to determine five elastic constants of the second and third orders included in the model relations. Calculation formulae are obtained and an example of determining the dependence of phase velocities on the preliminary deformation for polyamide 6 is given. The influence of preliminary deformations on polar diagrams of wave velocities is investigated.

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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