A tensorial classification of elastic waves

Abstract

Pure stress equations of motion of linear homogeneous anisotropic elastodynamics are used to present a classification of the plane stress progressive waves in an infinite body. A plane stress wave is decomposed into ‘‘normal’’ and ‘‘tangential’’ parts with respect to the wave front in such a way that: (i) both parts can propagate with the same velocity, (ii) the total stress energy of the wave is represented by the positive difference between ‘‘normal’’ and ‘‘tangential’’ stress energies, and (iii) pure ‘‘tangential’’ stress wave cannot propagate. The classification is consistent with and complementary to that of the displacement progressive waves, at least for homogeneous isotropic and transversely isotropic elastic media, and provides a number of new properties of the plane progressive waves in a general anisotropic elastic body.