title: Longitudinal shear wave and transverse dilatational wave in solids.
abstract: 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.
authors.affiliation: Inserm, U1032, LabTau, Lyon, F-69003, France stefan.catheline@inserm.fr.
authors.forename: S
authors.initials: S
authors.lastname: Catheline
authors.affiliation: Laboratorio de Acústica Ultrasonora, Instituto de Física, Facultad de Ciencias, Montevideo, Uruguay nicolas.benech@gmail.com.
authors.forename: N
authors.initials: N
authors.lastname: Benech