Longitudinal shear wave and transverse dilatational wave in solids

Dilatation wave involves compression and extension and is known as the curl-free solution of the elastodynamic equation. Shear wave on the contrary does not involve any change in volume and is the divergence-free solution. This letter seeks to examine the elastodynamic Green's function through this definition. By separating the Green's function in divergence-free and curl-free terms, it appears first that, strictly speaking, the longitudinal wave is not a pure dilatation wave and the transverse wave is neither a pure shear wave. Second, not only a longitudinal shear wave but also a transverse dilatational wave exists. These waves are shown to be a part of the solution known as coupling terms. Their special motion is carefully described and illustrated.