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The Quarterly Journal of Mechanics and Applied Mathematics 2000 53(3):343-361; doi:10.1093/qjmam/53.3.343
© 2000 by Oxford University Press
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Finite-amplitude inhomogeneous plane waves in a deformed Mooney–Rivlin material

M. DESTRADE1

( 1 Department of Mathematical Physics, University College Dublin, Belfield, Dublin 4, Ireland )

The propagation of finite-amplitude linearly-polarized inhomogeneous transverse plane waves is considered for a Mooney–Rivlin material maintained in a state of finite static homogeneous deformation. It is shown that such waves are possible provided that the directions of the normal to the planes of constant phase and of the normal to the planes of constant amplitude are orthogonal and conjugate with respect to the B-ellipsoid, where Bis the left Cauchy–Green strain tensor corresponding to the initial deformation. For these waves, it is found that even though the system is nonlinear, results on energy flux are nevertheless identical with corresponding results in the classical linearized elasticity theory. Byproducts of the results are new exact static solutions for the Mooney–Rivlin material.

Received 27 April, 1999. Revised 23 November, 1999.


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