Modeling of wave propagation in polycrystalline ice with hierarchical density gradients

Polycrystalline solids are composed of many small grains of varying sizes and crystallographic orientations. An elastic wave that propagates through such a material experiences distortion and attenuation. While the influence on propagation in random configurations can be captured with conventional statistical descriptors, the role of second-order features such as the hierarchical gradient in material properties has not been explored. In this paper, we optimize a numerical strategy based on Finite Elements and Local Max-Entropy approximants to characterize the role of grain density gradients on ultrasonic attenuation. We focus on ice as a model for mesoscale ordered configurations due to its relevance to the emerging technology of cryoultrasonics. Our simulations in one-and two-dimensional settings indicate that second-order descriptors are required to predict attenuation in polycrystalline ice. Furthermore, we define a novel parameter, based on the standard deviation of the speed of sound gradient distribution, which shows a quadratic relationship with the ultrasonic attenuation. The model results can be understood as a phase diagram for the design of metamaterials with specific ultrasonic scattering properties.