Wave propagation in heterogeneus media

Polycrystalline materials exhibit a microstructure made of grains with various sizes, shapes, and crystallographic orientations. Wave propagation behavior through such a medium exhibits distortions that are highly dependent on the spatial statistics of the microstructure, whose descriptors must be chosen carefully in order to make predictions.

In this work, we focus our study on the attenuation response of an ultrasonic wave propagating through a (macroscopically isotropic) polycrystalline ice microstructure.

Computational domain representing the ice microstructure.

We study how the attenuation varies when the density of the ice grains is modified. We introduce changes of density in the grains and therefore we affect the speed of sound 𝑐 (and therefore impedance). We apply a three-cycle Hann-windowed toneburst as a Dirichlet boundary condition. We compare the amplitude of emitted and received signals at the extremes of the 1D domain, where the speed of sound is kept constant. Between those measuring extremes, 163 grains of equal size are placed, mimicking a filter. The material property distributions of grains are realized through a vector of speeds 𝐜 with 163 different values of speed, whose variability stems from changes in density.

Attenuation coefficient as a function of the standard deviation of the difference in material properties

On the left side of the chart, small 𝜉 values signal configurations that minimize the gradient of density. These types of configurations can naturally occur due to atypical growing processes or due to gravity effects. In contrast, high values of 𝜉 represent configurations where the gradients between grains are maximized, and lead to very high values of attenuation. These extreme lower and higher 𝜉 configurations have been selected at random to create a representative curve and study the behavior of the attenuation over a relevant spectrum of orderings.

Publications

• Ghanbari, F., Rodriguez, E. G., Millán, D., Simonetti, F., Argüelles, A. P., & Peco, C. (2023). Modeling of wave propagation in polycrystalline ice with hierarchical density gradients. Finite Elements in Analysis and Design, 217, 103916. https://doi.org/10.1016/j.finel.2023.103916