  This study shows that the traditional definition of shear wave breaks the
shear stress reciprocity. By analyzing the displacement field for shear wave
and the motion equation of material element, it is found that the displacement
field is related to local rigid body rotation, and the local rigid body
rotation cannot be balanced by the stress state assumed in classical continuum
mechanics. It is also found that the displacement field caused by shear
deformation, which is neither divergence nor rotation, is replaced with that
caused by local rigid body rotation during the derivation of wave equation.
This indicates that the definition of shear wave is beyond the basic assumption
of continuum mechanics. The study modified the constitutive relation and
elastic tensor based on that the traditionally defined shear wave is objective.
The motion equation corresponding to shear wave is also derived. It is
concluded from the definition of traditional shear wave that the local rigid
body rotation should contribute stress and the shear stress reciprocity is not
prerequisite for nonpolar continuum.
