Reflexion and refraction of elastic waves in presence of separation

Abstract

The common assumption in treating the reflexion and refraction of elastic waves at the interface between two solids is that the bodies adhere, and that the required tensile tractions can be transmitted. This paper investigates the opposite case when the solids are pressed together, but do not adhere at all, so that the process for strong incident waves involves localized separation. It is shown that the reflected and refracted waves undergo a phase shift that depends on the extent of separation, and contain higher frequencies. The gaps open smoothly at the leading edges of the zones of separation, but close with discontinuous slopes at the trailing edges. This is due to the fact that the solids slam together as they come back into contact at the trailing edges. Accordingly, the interface tractions have jump discontinuities at the trailing edges. If the solids are not pressed together, steadily maintained incident waves see a free surface. The results also indicate, however, that a well-behaved steady state solution is not necessarily possible for all combinations of materials and angles of incidence.