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Spherical Harmonics Particle Shape Generator

  • Particle shape influences the hydro-mechanical behaviour of granular materials, e.g., packing density, shear strength, permeability.
  • Previous researches on particle shape effects mainly adopted ellipsoids, rod-like particles, or particle 'clusters'. These particles are either over-simplified or randomly selected.
  • We proposed a systemetic approach to randomly generate 3D particle morphologies with well-controled irregularith. This method depends on a series of Spherical Harmonics fuctions defined on a sphere.

Getting started

  • These instructions will illustrate the procedures to generate irregular particle shapes with SHPSG.

  • The algorithm depends on most common packages in Python.

  • Please refer to our papers on linking SHs coefficients and shape pactors Link and SHs coeffecients random generation method

Particle shape

  • Particle shape is a multi-scale feature and usually described at three scales, i.e. form, roundness and roughness.

  • Spherical Harmonics decompose particle shape features into several degrees. Our study shows particle form and roundness are well represented at degree 1 and 8, respectively.

  • Particle form is defined by three principal dimensions that perpendicular to each other: a$\geq$b$\geq$c. Elongation index Ei = b/a, flatness index Fi = c/b.

  • Particle roundness is related to SHs coefficients $D_{2-8}$. Higher $D_{2-8}$ value leads to lower roundness.

  • Roughness is related to SHs coefficients $D_{9-15}$. Note that we did not show examples of roughness control.

  • The particles are represented by surface meshes with 320 triangular elements. Finer mesh could be used by increasing the mesh subdivision number. A finer surface mesh is needed to show the influence of $D_{9-15}$.

Examples

A sphere: Ei = 1; Fi = 1; $D_{2-8} = 0$, and $D_{9-15} = 0$.

An elipsoid: Ei = 1; Fi = 0.5; $D_{2-8} = 0$, and $D_{9-15} = 0$.

An elipsoid: Ei = 0.8; Fi = 0.5; $D_{2-8} = 0$, and $D_{9-15} = 0$.

Angular particle: Ei = 1; Fi = 1; $D_{2-8} = 0.2$, and $D_{9-15} = 0$.

More angular particle: Ei = 1; Fi = 1; $D_{2-8} = 0.4$, and $D_{9-15} = 0$.

Authors

  • Deheng Wei - developed first Matlab code in combination with SPHARM-PDM
  • Budi Zhao - supervised Deheng and developed the standalone Python code
  • Jianfeng Wang - principal investigator for this project

License

This project is licensed under the MIT License - see the LICENSE.md file for details

Acknowledgments

  • Icosahedron and subdivision code based on Matlab code by Wil O.C. Ward Link

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