Scattering of elastic waves by a sphere with orthorhombic anisotropy and application to polycrystalline material characterization-Supplementary Documents

We have included electronic supplementary materials to support our calculations, which consist of three files:

1. "Transformation of constitutive relations.nb": This Mathematica code transforms the constitutive relation of an orthorhombic medium from Cartesian coordinates to spherical coordinates.

2. "T matrix elements.zip": This set of Mathematica codes calculates $\mathbf{T}$ matrix elements of a sphere with orthorhombic symmetry, explicitly for the low frequency limit. We have organized each decoupled system of equations, as explained in the paper, into separate files. However, in the case of section 4.5 of the paper with $m=0,2$, $\sigma=e$, and even values of $l$, the system of equations becomes too large. To address this, first the system of equations are driven and then solved in separate files for the scattered P waves of order $m=0$ and $l=0$, scattered P-SV waves of order $m=0$ and $l=2$, and scattered P-SV waves of order $m=2$ and $l=2$.

3. "Explicit Wave Numbers in Polycrystals.nb": This is another Mathematica code that utilizes all the $\mathbf{T}$ matrix elements evaluated in the second file and expressed in the paper. It calculates effective wave numbers for polycrystalline materials consisting of equiaxed randomly oriented crystals with orthorhombic symmetry, explicitly for the low-frequency limit.

We hope that these supplementary materials will provide readers with a better understanding of our methods and results and enable them to reproduce our findings if they wish to do so.