On the transition between slip and rigid boundary conditions between two solid media

Abstract

In order to describe the transition between slip and rigid boundary conditions, a model with a thin interphasial viscoelastic layer is introduced. By changing the relaxation time (ωτ), the transition from a viscous liquid to a solid layer is observed. When the interface layer is in the liquid state with very small shear nodulus the shear stress components on the boundary vanish, resulting in a slip boundary condition. On the other hand, after the layer is solidified, the two semispaces become welded with the transition of shear and longitudinal stresses to one another. It is shown that the ratio of a hydrodynamic boundary layer thickness to the interface layer thickness plays a major role in this transition. A simple approximate equation for the reflection coefficient from the interface is derived and compared to the exact solutions for different transitional stages of the boundary condition. Theoretical predictions are compared to experimental results.