The generalized self-consistent method (GSCM) is used in conjunction with a computational finite element method to calculate the anisotropic effective moduli of a medium containing damage consisting of microcracks with an arbitrary degree of alignment. Since cracks respond differently under different external loads, the moduli of the medium subjected to tension, compression and an initially stress-free state are evaluated and shown to be significantly different, which will further affect the wave speed inside the damaged media. There are four independent material moduli for a 2-D plane stress orthotropic medium in tension or compression, and seven independent material moduli for a 2-D plane stress orthotropic cracked medium, which is initially stress free. When friction exists between the cracks’ surfaces, it further changes the effective moduli. Numerical methods are used to take into account crack face contact and friction.

Direct numerical simulations of waves traveling through microcrack-damaged media are conducted and the results are compared to analytical and effective medium calculations to determine the applicability of the latter for studying wave propagation. Both tensile and compressive waves and various angular distributions of randomly-located cracks are considered. In direct simulations of unidirectional wave propagation, the relationships between the input wavelength and the output wave speed and output signal strength are studied. The numerical simulations show that the wave speed is nearly constant when 1/ka > 60 for tensile waves and 1/ka >10 for compressive waves, where k is the wave number and a is the average half-crack length. The direct simulations also show that when the input wavelength is much longer than the crack length, 1/ka > 60 , the wave can pass through the damaged medium relatively unattenuated. On the other hand, when the input wavelength is shorter than a “cut off” wave length, the output wave magnitude decreases linearly with the input wavelength. The effective medium wave speed and magnitude calculations are not dependent on the input wavelength and therefore the results correspond well with the numerical simulations for large 1/ka. This suggests a minimum wavelength for which the homogenized methods can be used for studying these problems. In a 2D wave propagation study, the analytically predicted wave fronts are compared with those from the direct numerical simulations and those predicted by the effective medium calculations. The results show that the effective material models predict relatively accurate wave fronts in planar wave propagation through microcrack-damaged media.