Elastic wave propagation through a distribution of dislocations

We study the coherent propagation of an elastic wave in a two-dimensional continuous elastic medium filled with dislocation arrays randomly distributed and oriented in space. This configuration reasonably mimics grain boundaries in polycrystals. Interest is in evaluating the plastic contributions to the multiple scattering of waves in polycrystals that may superpose to other known scattering processes, like scattering due to inhomogeneities of elastic properties among grains. Calculations are performed in a multiple scattering formalism, based on the derivation of the so-called mass operator, in the approximation of weak scattering. We find that sound attenuation increases when the frequency decreases, a trend opposite to the usual behavior, suggesting that dislocations could sensibly modify the acoustic properties of materials at low frequency.