Finite-Amplitude Waves in Mooney-Rivlin and Hadamard Materials

  • Philippe Boulanger
  • Michael Hayes
Part of the International Centre for Mechanical Sciences book series (CISM, volume 424)


These lectures deal with the the propagation of finite amplitude plane waves in Mooney-Rivlin and Hadamard elastic materials which are maintained in a state of arbitrary static homogeneous deformation. Exact plane wave solutions are presented for arbitrary propagation direction. The energy properties of these waves are investigated.


Longitudinal Wave Wave Speed Finite Amplitude Principal Plane Principal Stretch 
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  1. Beatty, M. (1987). Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl. Mech. Rev. 40: 1699–1734.CrossRefADSGoogle Scholar
  2. Born, M., and Wolf, E. (1980). Principles of Optics. Oxford: Pergamon, 6th edition.Google Scholar
  3. Boulanger, Ph., and Hayes, M. (1992). Finite-amplitude waves in deformed Mooney-Rivlin materials. Q. JI. Mech. appl. Math. 45: 575–593.MathSciNetCrossRefMATHGoogle Scholar
  4. Boulanger, Ph., and Hayes, M. (1993). Bivectors and Waves in Mechanics and Optics. London: Chapman and Hall.MATHGoogle Scholar
  5. Boulanger, Ph., Hayes, M., and Trimarco, C. (1994). Finite-amplitude plane waves in deformed Hadamard materials. Geophys. J. Int. 118: 447–458.CrossRefADSGoogle Scholar
  6. Boulanger, Ph., and Hayes, M. (1995a). Further properties of finite-amplitude plane waves in deformed Mooney-Rivlin materials. Q. JI. Mech. appl. Math. 48: 427–464MathSciNetCrossRefMATHGoogle Scholar
  7. Boulanger, Ph., and Hayes, M. (1995b). The common conjugate directions of plane sections of two concentric ellipsoids. In Casey, J., and Crochet, M. J., eds., Theoretical, experimental, and numerical contributions to the mechanics of fluids and solids. Special Issue of Z Angew. Math. Phys., 46: 356–371CrossRefGoogle Scholar
  8. Boulanger, Ph., and Hayes, M. (1996). Largest and least phase and energy speeds for plane waves in deformed Mooney-Rivlin materials. In Batra, R. C., and Beatty, M. F., eds., Contemporary research in the mechanics and mathematics of materials. Barcelona: CIMNE. 145–150.Google Scholar
  9. Boulanger, Ph., and Hayes, M. (1997). Wave propagation in sheared rubber. Acta mechanica 122: 75–87.MathSciNetCrossRefMATHGoogle Scholar
  10. Carroll, M. M. (1967). Some results on finite amplitude waves. Acta Mechanica 3: 167–181.CrossRefGoogle Scholar
  11. Chadwick, P., and Ogden, R. W. (1971). A theorem of tensor calculus and its applications to isotropic elasticity. Arch. Rational Mech. Anal. 44: 54–68.MathSciNetMATHADSGoogle Scholar
  12. Currie, P., and Hayes, M. (1969). Longitudinal and transverse waves in finite elastic strain. Hadamard and Green materials. J. Inst. Maths Applies 5: 140–161.CrossRefMATHGoogle Scholar
  13. Ericksen, J. L. (1953). On the propagation of waves in isotropic incompressible perfectly elastic materials. J. Ration. Mech. Anal. 2: 329–337.MathSciNetMATHGoogle Scholar
  14. Green, A. E. (1963). A noté on wave propagation in initially deformed bodies. J. Mech. Phys. Solids 11: 119–126.MathSciNetCrossRefADSGoogle Scholar
  15. Hadamard, J. (1903). Leçons sur la propagation des ondes et les équations de l’hydrodynamique. Paris: Hermann (reprinted, New York: Chelsea, 1949 ).Google Scholar
  16. Hayes, M. (1968). A remark on Hadamard materials. Q. Jl. Mech. appl. Math. 21: 141–146.CrossRefMATHGoogle Scholar
  17. Hayes, M. (1980). Energy flux for trains of inhomogeneous plane waves. Proc. R. Soc. Lond. A370: 417–429.CrossRefMATHADSGoogle Scholar
  18. Hayes, M., and Rivlin, R. S. (1971). Energy propagation for finite amplitude shear waves. ZAMP 22: 1173–1176.CrossRefADSGoogle Scholar
  19. John, F. (1966). Plane elastic waves of finite amplitude. Hadamard materials and harmonic materials. Communs pure appl. Math. 19: 309–341.CrossRefMATHGoogle Scholar
  20. Landau, L. D., and Lifschitz, E. M. (1960). Electrodynamics of Continuous Media. Oxford: Pergamon.MATHGoogle Scholar
  21. Musgrave, M. J. P. (1970). Crystal Acoustics. San Francisco: Holden-Day.MATHGoogle Scholar
  22. Ogden, R. W. (1970). Waves in isotropic elastic materials of Hadamard, Green, or harmonic type. J. Mech. Phys. Solids 18: 149–163.MathSciNetCrossRefMATHADSGoogle Scholar
  23. Partington, J. R. (1953). An advanced treatise on physical chemestry, Vol. 4. London: Longmans, Green and Co.Google Scholar
  24. Whitham, G. B. (1974). Linear and nonlinear waves. New York: J.Wiley and Sons.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Philippe Boulanger
    • 1
  • Michael Hayes
    • 2
  1. 1.Départment de MathématiqueUniversité Libre de BruxellesBelgium
  2. 2.Department of Mathematical PhysicsUniversity College DublinIreland

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