Abstract
Conditions are obtained on the strain-energy functions of compressible isotropic homogeneous hyperelastic solids which admit the propagation of finite amplitude transverse waves, without accompanying coupled longitudinal waves, or which admit the simultaneous propagation of uncoupled transverse and longitudinal waves. Three types of transverse waves are considered: plane shear waves, axisymmetric anti-plane shear waves and azimuthal shear waves. Static axisymmetric anti-plane shear and static azimuthal shear, which result in isochoric deformation, are also considered for comparison with the corresponding wave propagation problems.
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