The non-uniform motion of a thin smooth rigid inclusion through an elastic solid

A two-dimensional example of non-uniform motion by a smooth, relatively thin, symmetric rigid inclusion through an elastic solid is analyzed. Integral solutions to the related boundary-initial value problem are obtained for the case of edge speeds bounded by the dilatational wave speed at large times. The wavefront patterns, including the possibility of Mach waves, are noted. Some attention is focused on the case of the straight wedge, and logarithmic singularities are found at its edge for subsonic speeds.