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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.

In a previous paper (3), Currie and Hayes showed that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.Here, we recover this result and obtain explicit expressions for the speeds of the two waves in terms of the angles that n makes with special directions, called 'acoustic axes'. These are the only directions such that the two wave speeds are equal. They are determined only by the basic static deformation of the material. There are two such directions if this deformation is triaxial, and one if it is biaxial.Then, it is shown that, although the theory is nonlinear, the superposition of the two waves propagating along any direction is also a solution. In particular, for propagation along an acoustic axis, elliptically and circularly polarized finite-amplitude waves are possible.Finally, the energy flux and energy density of the waves are considered. © 1992 Oxford University Press.

The nonlinear elastic response of a class of materials for which the deformation is subject to an internal material constraint described in experiments by James F. Bell on the finite deformation of a variety of metals is investigated. The purely kinematical consequences of the Bell constraint are discussed, and restrictions on the full range of compatible deformations are presented in geometrical terms. Then various forms of the constitutive equation relating the stress and stretch tensors for an isotropic elastic Bell material are presented. Inequalities on the mechanical response functions are introduced. The importance of these in applications is demonstrated in several examples throughout the paper.