par Boulanger, Philippe ;Hayes, Michael
Référence Quarterly Journal of Mechanics and Applied Mathematics, 48, 3, page (427-464)
Publication Publié, 1995-08
Article révisé par les pairs
Résumé : In a previous paper, Currie and Hayes (J. Inst. Maths Applics 5 (1969) 140-161) showed that two linearly polarized finite-amplitude plane shear waves may propagate with constant speeds along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation. Later, Boulanger and Hayes (Q. Jl Mech. appl. Math 45 (1992) 575-593), using special directions called 'acoustic axes', obtained explicit expressions for the polarization directions and the phase speeds of these waves in terms of the propagation direction.Here further properties of these waves are obtained. An energy-flux velocity vector is introduced and a duality between slowness and energy-flux velocity is exhibited. The slowness and ray surfaces are obtained and their singular points and singular tangent planes are studied. As in crystal optics and crystal acoustics, it follows that cones of internal and external conical refraction may be introduced.Also, it is shown that for a given direction of the energy-flux velocity ('ray direction'), two plane shear waves may propagate. Introducing new special directions called 'ray axes', explicit expressions are obtained for the various properties of these waves in terms of the ray direction. The duality between the results for a given propagation direction and for a given ray direction is clearly brought out.Finally, it is shown that a finite-amplitude plane shear wave is uniquely determined by its polarization direction, provided this direction is not along a principal axis of the basic static homogeneous deformation. Indeed all the properties of such a wave may be expressed in terms of its polarization direction. © 1995 Oxford University Press.

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