Two basic wave propagation problems for the non-uniform motion of displacement discontinuities across a bimaterial interface

The splitting of laminated materials is often achieved by, in effect, moving more rigid solids through the material or by causing a shear tearing characterized by the relative slip of adjacent material points. Both processes may take place across the bimaterial interfaces of the laminate. Moreover, both processes involve the motion of displacement discontinuities. This article examines basic wave propagation problems for the non-uniform motion of two arbitrary displacement discontinuities in perfectly-bonded half-planes along paths normal to the interface. The discontinuities impose relative displacements which are, respectively, normal to and along the path. Complete solutions are derived in forms which allow identification of each component of the reflection and transmission-complicated wave pattern. The dependence of these components on specific aspects of the discontinuity behavior can be noted. Finally, two physical examples, the motions of a rigid wedge and an edge dislocation across the interface are studied. It is found that the singularity order and direction of characteristic stresses can be affected by crossing the interface.