MATCHED ASYMPTOTIC EXPANSIONS FOR 2 DIMENSIONAL ELASTODYNAMIC DIFFRACTION BY CRACKS

For two-dimensional diffraction by a crack in an elastic solid it is shown that the geometrical theory of diffraction represents an asymptotic solution to the equations of linear elastodynamics, which satisfies the boundary conditions of vanishing tractions on the crack faces. The analysis consists of matching an outer solution valid far from the edge of the crack to an inner solution valid near the crack edge. The outer solution fails on the boundary of the region containing direct rays, as well as on the boundaries of the regions containing reflected rays of longitudinal and transverse motion. Uniform corrections to the theory are given which provide a smooth transition across these boundaries. © 1979.