A higher order approximation to the wave propagation constants for a cracked solid

Expressions are available in the literature for the propagation constants of a ‘mean’ wave travelling in a material with a random distribution of cracks. These are approximations for small crack density and crack dimensions small compared with a wavelength. The formulae provided to second order in crack density by the method of smoothing are here extended to the case where the cracks consist of two or more sets, aligned in different directions.