Finite-amplitude plane waves in deformed Hadamard elastic materials

Abstract

SUMMARY It has been shown previously (John 1966; Currie & Hayes 1969) that Hadamard compressible elastic materials are the only ones for which three linearly polarized finite-amplitude plane waves, one longitudinal and two transverse, may propagate in any direction when the material is maintained in a state of arbitrary static finite homogeneous deformation. Here we first obtain simple explicit expressions for the three wave speeds and a simple characterization of the polarization directions of the transverse waves. Also, although the theory is non-linear, it is seen that the three waves may be superposed: they do not interact. Special directions, called acoustic axes, are introduced. These are the only directions along which circularly polarized transverse waves may propagate. They are determined only by the basic static deformation of the material. Results are expressed in terms of the angles that the propagation direction makes with the acoustic axes. Then, the energy flux and energy density of the waves are considered. Relations between the projection on to the propagation direction of the energy flux vector and the energy density are derived for each individual wave. Finally, periodic transverse waves are considered.