Three propagation modes of elastic stress waves

The translational and rotational deformation of a deformed body in the scope of infinite simal deformation are analyzed. With the use of the momentum and angular momentum conservation equations, the constitutive relation of couple stress and the constitutive relation of isotropic elastic body are applied, and a volumetric wave, a rotational wave as well as a deviatoric wave are found to travel in isotropic elastic solids. The rotational and the deviatoric waves are governed by the four-order wave motion equations, whereas they are provided for different kinematic behavior and stress states. The four-order rotational wave and deviatoric wave propagated in the isotropic elastic solid no more rely on a constant speed. Only the volumetric wave and the two-order deviatoric wave with constant speeds are propagated in elastic solids without the rotational motion. In the three wave modes,the volumetric wave is identical with the conventional stress wave theory, the rotational wave of four-order equation may be reduced to the rotational wave of two-order equation formally, the deviatoric wave of four-order equation can be reduced to the deviatoric wave of two-order which differs completely from the two-order shear wave in the conventional stress wave theory. With a view on the deformation-stress relation and energy propagation, some problems of the conventional rotational and shear waves are pointed out.