  We investigate the elastic wave propagation in various hyperelastic materials
which subjected to simple-shear deformation. Two compressible types of three
conventional hyperelastic models are considered. We found pure elastic wave
modes can be obtained in compressible neo-Hookean materials constructed by
adding a bulk strain energy term to the incompressible strain energy function.
Whereas for the compressible hyperelastic models which are reformulate into
deviatoric and hydrostatic parts, only quasi modes can propagate, with abnormal
ray directions can be observed for longitudinal waves. Moreover, the influences
of material constants, material compressibility and external deformations on
the propagation and refraction for elastic waves in these hyperelastic models
are systematically studied. Numerical simulations are carried out to validate
the theoretical results. This investigation may open a promising route for the
realization of next generation metamaterials and novel wave manipulation
devices.
