Some comments on the dynamic properties of anisotropic and strongly anisotropic pre-stressed elastic solids

The effect of pre-stress on the propagation of small amplitude waves in an incompressible, transversely isotropic elastic solid is discussed in respect of the most general appropriate strain energy function. A simple set of sufficient conditions is noted which ensures that two real wave speeds exist for all directions of propagation. In the case of bi-axial primary deformations, and for propagation within each principal plane of the homogeneous primary deformation, the propagation condition is factorised and conditions which are both necessary and sufficient to ensure the existence of two real wave speeds are established. The paper also includes some graphical illustrations of the associated slowness and wave surfaces and discussion of the strongly anisotropic case, for which the extensional modulus along the preferred fibre direction is much larger than other material parameters.