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The Incremental Shear Modulus in an Incompressible Elastic Material

  • K. N. Sawyers
  • R. S. Rivlin

Summary

The incremental shear modulus is calculated for infinitesimal shear of an incompressible isotropic elastic material in a state of pure homogeneous deformation. Necessary and sufficient conditions that it be positive are obtained. These conditions are related to the Hadamard conditions for propagation of a wave of infinitesimal amplitude in the deformed material.

Keywords

Vector Position Simple Shear Sinusoidal Wave Principal Plane Hadamard Condition 
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Sommario

Il modulo trasversale incrementale è calcolato per una deformazione trasversale inflnitesima di un materiale elastico isotropico ed incompressibile in uno stato di deformazione pura ed omogenea. Si ottengono le condizioni necessarie e sufflcienti per un modulo positivo. Sipossono riferire queste condizioni alle condizioni di Hadamard per la propagazione di un ’onda di ampiezza inflnitesima in un materiale deformato.

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References

  1. [1]
    Sawyers K. N., Rivlin R. S., Developments in Mechanics 7, Proc. 13th Midwestern Mechanics Conference 321 (1973).Google Scholar
  2. [2]
    Sawyers K. N., Rivlin R. S., Journal of Applied Mathematics and Physics 28, 1045 (1977).CrossRefGoogle Scholar
  3. [3]
    Sawyers K. N., Rivlin R. S., Int. J. Solids Structures 9, 607 (1973).CrossRefGoogle Scholar
  4. [4]
    Sawyers K. N., Rivlin R. S., Mechanics Research Comunications 5, 211 (1978).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • K. N. Sawyers
    • 1
  • R. S. Rivlin
    • 1
  1. 1.Center for the Application of MathematicsLehigh UniversityBethlehemUSA

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