Elastic stress of moving dislocations in finite crystals

The elastic stress of a single crystal with finite dimensions is investigated by means of the linear continuum theory; external forces and dislocation motion are assumed to be known. A formal solution is derived with a Green's dyadic. The dyadic is expanded in a series, the first term of which delivers the well-known solution for infinite crystals, the following terms describe successive reflections of sound at the surface of the finite crystal. They can be computed by iteration. This expansion corresponds to the physical situation of pulse-echo-experiments. Fourier transforms lead to analogous expressions describing the influence of the surface on time-periodic dislocation experiments.