Applied Scientific Research, Section A

, Volume 12, Issue 2, pp 151–167 | Cite as

Incremental elastic coefficients of an isotropic medium in finite strain

  • M. A. Biot


Incremental elastic coefficients are derived for an isotropic medium in a state of finite initial strain. The analysis is based on concepts and methods developed by the author in earlier publications1)2)3)5) which require only elementary procedures and bring to light the physical significance of the results. Remarkably simple formulas for the incremental shear coefficients are established. For comparison the same results are derived by an alternate procedure using Riemannian tensors and the calculation is shown to be much more elaborate. Application is made to the particular case of second order elasticity theory and expressions derived for the incremental coefficients including the correction terms of the first order in the initial strain. This provides a complete theory of first order correction for acoustic propagation under initial stress.


Principal Stress Initial Stress Principal Direction Isotropic Medium Initial Strain 
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  1. 1).
    Biot, M. A., Theory of Elasticity with Large Displacements and Rotations. Proc. Fifth Int. Cong. Appl. Mech. 1938.Google Scholar
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    Biot, M. A., Phil. Mag. Sec. 7,XXVII (1939) 468.Google Scholar
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    Biot, M. A., Z. Angew. Math. Mech.20 (1940) 89.CrossRefMathSciNetGoogle Scholar
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    Murnaghan, F. D., Amer. J. Math.59 (1937) 235.MATHCrossRefMathSciNetGoogle Scholar
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    Biot, M. A., J. Appl. Phys.11 (1940) 520.MathSciNetADSGoogle Scholar
  6. 6).
    Brillouin, L., Les Tensenrs en Mécanique et en Elasticité, Masson et Cie., 1938, Dover Publications, 1946.Google Scholar
  7. 7).
    Sokolnikoff, I. S., Tensor Analysis, John Wiley & Sons, New York, 1951 (Chapter 6, p. 302).MATHGoogle Scholar

Copyright information

© Martinus Nijhoff, The Hague/Kluwer Academic Publishers 1963

Authors and Affiliations

  • M. A. Biot
    • 1
  1. 1.New YorkU.S.A.

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