Quasistatic approximation to the scattering of elastic waves by a circular crack

The elastic-wave scattering by a flat crack can be represented by an integral expression involving displacement and strain on the surface of the crack. We have explored the use of a modified static solution as an approximation to the displacement field of a penny-shape crack in the long-wavelength regime and then studied numerically how well it connects with the low-freqency limit of the diffraction regime. Comparisons between this and several other existing approximations are made. We conclude that this quasistatic approximation is useful practically in both the long-wavelength and beginning diffraction regime.