Abstract
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.
Lectures presented by Ph. Boulanger
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References
Beatty, M. (1987). Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl. Mech. Rev. 40: 1699–1734.
Born, M., and Wolf, E. (1980). Principles of Optics. Oxford: Pergamon, 6th edition.
Boulanger, Ph., and Hayes, M. (1992). Finite-amplitude waves in deformed Mooney-Rivlin materials. Q. JI. Mech. appl. Math. 45: 575–593.
Boulanger, Ph., and Hayes, M. (1993). Bivectors and Waves in Mechanics and Optics. London: Chapman and Hall.
Boulanger, Ph., Hayes, M., and Trimarco, C. (1994). Finite-amplitude plane waves in deformed Hadamard materials. Geophys. J. Int. 118: 447–458.
Boulanger, Ph., and Hayes, M. (1995a). Further properties of finite-amplitude plane waves in deformed Mooney-Rivlin materials. Q. JI. Mech. appl. Math. 48: 427–464
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: 356–371
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.
Boulanger, Ph., and Hayes, M. (1997). Wave propagation in sheared rubber. Acta mechanica 122: 75–87.
Carroll, M. M. (1967). Some results on finite amplitude waves. Acta Mechanica 3: 167–181.
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.
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.
Ericksen, J. L. (1953). On the propagation of waves in isotropic incompressible perfectly elastic materials. J. Ration. Mech. Anal. 2: 329–337.
Green, A. E. (1963). A noté on wave propagation in initially deformed bodies. J. Mech. Phys. Solids 11: 119–126.
Hadamard, J. (1903). Leçons sur la propagation des ondes et les équations de l’hydrodynamique. Paris: Hermann (reprinted, New York: Chelsea, 1949 ).
Hayes, M. (1968). A remark on Hadamard materials. Q. Jl. Mech. appl. Math. 21: 141–146.
Hayes, M. (1980). Energy flux for trains of inhomogeneous plane waves. Proc. R. Soc. Lond. A370: 417–429.
Hayes, M., and Rivlin, R. S. (1971). Energy propagation for finite amplitude shear waves. ZAMP 22: 1173–1176.
John, F. (1966). Plane elastic waves of finite amplitude. Hadamard materials and harmonic materials. Communs pure appl. Math. 19: 309–341.
Landau, L. D., and Lifschitz, E. M. (1960). Electrodynamics of Continuous Media. Oxford: Pergamon.
Musgrave, M. J. P. (1970). Crystal Acoustics. San Francisco: Holden-Day.
Ogden, R. W. (1970). Waves in isotropic elastic materials of Hadamard, Green, or harmonic type. J. Mech. Phys. Solids 18: 149–163.
Partington, J. R. (1953). An advanced treatise on physical chemestry, Vol. 4. London: Longmans, Green and Co.
Whitham, G. B. (1974). Linear and nonlinear waves. New York: J.Wiley and Sons.
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Boulanger, P., Hayes, M. (2001). Finite-Amplitude Waves in Mooney-Rivlin and Hadamard Materials. In: Hayes, M., Saccomandi, G. (eds) Topics in Finite Elasticity. International Centre for Mechanical Sciences, vol 424. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2582-3_4
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DOI: https://doi.org/10.1007/978-3-7091-2582-3_4
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