FINITE-AMPLITUDE WAVES IN DEFORMED MOONEY-RIVLIN MATERIALS

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.