RESUMO
The elastodynamic behavior of polycrystalline cubic materials is studied through the fundamental propagation properties, the attenuation and wave speed, of a longitudinal wave. Predictions made by different analytical models are compared to both numerical and experimental results. The numerical model is based on a three-dimensional Finite Element (FE) simulation which provides a full-physics solution to the scattering problem. The three main analytical models include the Far-Field Approximation (FFA), the Self-Consistent Approximation (SCA) to the reference medium, and the herein derived Second Order Approximation (SOA). The classic Stanke and Kino model is also included, which by comparison to the SOA, reveals the importance of the distribution of length-scales described in terms of the two-point correlation function in determining scattering behavior. Further comparison with the FE model demonstrates that the FFA provides a simple but satisfactory approximation, whereas the SOA shows all-around excellent agreement. The experimental wave velocity data evaluated against the SOA and SC reveal a better agreement when the Voigt reference is used in second order models. The use of full-physics numerical simulations has enabled the study of wave behavior in these random media which will be important to inform the ongoing development of analytical models and the understanding of observations.
RESUMO
The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.