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Propagation of antiplane coherent wave in solids containing randomly and uniformly distributed cracks is studied by calculating the associated effective wave number. Attention is focused on the influence of crack opening and orientation. Strip-like cracks or empty elliptical cavities are either mutually parallel or randomly oriented, and their surfaces are stress-free. Different multiple-scattering formulations for the effective wave number, in terms of the far-field displacement scattered by a single crack in the matrix, are compared for various crack systems. They coincide at low crack density and show similar trends when the crack density increases. Simple analytical estimates enable a direct evaluation of the crack density from the speed and attenuation of the coherent wave. In the low- and high-frequency ranges, the effective wave speed and attenuation appear to be mainly governed by the projection of cracks on the incident plane wave front.
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Caleap et al. (2009) studied this question.
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