Journal of Elasticity

, Volume 55, Issue 2, pp 163–166 | Cite as

Finite-Amplitude Inhomogeneous Plane Waves of Exponential Type in Incompressible Elastic Materials

  • M. Destrade

Abstract

It is proved that elliptically polarized finite-amplitude inhomogeneous plane waves may not propagate in an elastic material subject to the constraint of incompressibility. The waves considered are harmonic in time and exponentially attenuated in a direction distinct from the direction of propagation. The result holds whether the material is stress-free or homogeneously deformed.

finite amplitude inhomogeneous plane waves elliptical polarization incompressibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ph. Boulanger and M. Hayes, Bivectors and Waves in Mechanics and Optics. Chapman & Hall, London (1993).MATHGoogle Scholar
  2. 2.
    A.E. Green, A note on wave propagation in initially deformed bodies. J. Mech. Phys. Solids 11 (1963) 119-126.MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    P. Currie and M. Hayes, Longitudinal and transverse waves in finite elastic strain. Hadamard and Green materials. J. Inst. Math. Appl. 5 (1969) 140-161.MATHGoogle Scholar
  4. 4.
    Ph. Boulanger and M. Hayes, Finite-amplitude waves in deformed Mooney-Rivlin materials. Quart. J. Mech. Appl. Math. 45 (1992) 575-593.MATHMathSciNetGoogle Scholar
  5. 5.
    M. Hayes and R.S. Rivlin, Surface waves in deformed elastic materials. Arch. Rational. Mech. Anal. 8 (1961) 383-380.Google Scholar
  6. 6.
    J.N. Flavin, Surface waves in prestressed Mooney material. Quart. J. Mech. Appl. Math. 16 (1963) 441-449.MATHMathSciNetGoogle Scholar
  7. 7.
    J.A. Belward, Some dynamic properties of a prestressed incompressible hyperelastic material. Bull. Austral. Math. Soc. 8 (1973) 61-73.MATHCrossRefGoogle Scholar
  8. 8.
    J.A. Belward and S.J. Wright, Small-amplitude waves with complex wave numbers in a prestressed cylinder of Mooney material. Quart. J. Mech. Appl. Math. 40 (1987) 383-399.MATHGoogle Scholar
  9. 9.
    P. Borejko, Inhomogeneous plane waves in a constrained elastic body. Quart. J. Mech. Appl. Math. 40 (1987) 71-87.MATHGoogle Scholar
  10. 10.
    Ph. Boulanger and M. Hayes, Propagating and static exponential solutions in a deformed Mooney-Rivlin material. In: M. Carroll and M. Hayes (eds), Nonlinear Effects in Fluids and Solids. Plenum Press, New York (1996) pp. 113-123.Google Scholar
  11. 11.
    M. Hayes, Inhomogeneous plane waves. Arch. Rational Mech. Anal. 85 (1984) 41-79.MATHMathSciNetADSCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • M. Destrade
    • 1
  1. 1.Mathematical PhysicsUniversity College DublinBelfield, Dublin 4Ireland E-mail

Personalised recommendations