Analysis of boundary conditions for elastic wave interaction with an interface between two solids

The boundary conditions for an interface between two solids are analyzed to model a thin viscoelastic interface layer. Boundary conditions that relate stresses and displacements on both sides of the interface are obtained as an asymptotic representation of three-dimensional solutions for an interface layer in the limit of small wavelength to thickness ratio. The interface boundary conditions obtained include interface stiffnesses and inertia and terms involving coupling between normal and tangential stresses and displacements. The applicability of such boundary conditions is analyzed by comparison with exact solutions for ultrasonic wave reflection. Fundamental boundary conditions are introduced where only one transverse or normal mass or stiffness is included. It is shown that the solution for more exact interface boundary conditions which include two inertia elements and two stiffness elements can be decomposed into a sum of fundamental solutions. The transition between welded and slip boundary conditions on an interface with a thin viscous layer is also analyzed as a function of interface thickness, viscous skin depth, and frequency.