Interaction of elastic waves with the unilateral interface between a layer and a half-space (Q1579782)

Linear elasticity deals with the so-called bilateral constraints, when traction and displacements are continuous when passing through the separation surface of two media. This corresponds, by example, to the case when two solids are welded. On the other side, when two media are pressed one against the other, a new type of constraint can occur, the so-called unilateral one. Here, such a case is discussed: a layer of thickness \(H\) is pressed with pressure \(p_\infty\) against a half-space. Bot media are linear and isotropic, frictional effects are neglected. A plane pressure wave comes on the boundary from the half-space at the angle \(\theta_0\) (less than the critical one). Then, as is known, a separation zone and a contact zone are formed. The problem is to find the fields in two media and conditions under which a separation zone is formed. A set of two linear functional equations allows to obtain the solution and to derive conditions for the appearance of the interface zone in terms of some governing parameters: \(p_\infty\), \(A_0\) (the pressure amplitude of the incoming wave), the layer thickness, the wave frequency etc. Finally, the author presents diagrams illustrating various situations. Unfortunately, the English of the paper is not of the same quality as the contents.