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Spherical Harmonics Particle Shape Generator - SHPSG

  • Particle shape influences the properties of granular materials, e.g., packing density, shear strength, permeability.

  • Existing methods generating irregular particle shapes are sometimes over-simplified, e.g., ellipsoids, rod-like particles, or particle 'clusters'.

  • This algorithm randomly generates 3D particle morphologies of user-specified irregularity with Spherical Harmonics.

  • This algorithm systematically controls shape irregularity at different scales, e.g., form, roundness and roughness.

Getting started

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

  • The algorithm depends on most common packages in Python.

  • The theories were introduced in two papers: rotational-invirant analysis Link and SHs coeffecients random generation method Link

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 different scales, SH 'degrees'. For example, particle roundness is well represented with SH coefficients from degree 2 to 8.

  • Particle form is defined by three principal dimensions that perpendicular to each other: a$\geq$b$\geq$c. We control two aspect ratios: elongation index Ei = b/a, and flatness index Fi = c/b.

  • Particle roundness reflects curvatures at corners. A higher roundness particle has a lower $D_{2-8}$.

  • Roughness characterizes surface featureas between corners. A higher roughness particle has a lower $D_{9-15}$.

  • 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 $D_{9-15}$.

Parameter control examples

A sphere: Ei = 1; Fi = 1; D2_8 = 0; D9_15 = 0

Oblate spheroid: Ei = 1; Fi = 0.5; D2_8 = 0; D9_15 = 0

Probalate spheroid: Ei = 0.5; Fi =1; D2_8 = 0; D9_15 = 0

Low angularity: Ei = 1; Fi = 1; D2_8 = 0.1; D9_15 = 0

High angularity: Ei = 1; Fi = 1; D2_8 = 0.4; D9_15 = 0

Random generated angular particles

Ei = 1; Fi = 1; D9_15 = 0

D2_8 = 0.1

D2_8 = 0.2

D2_8 = 0.3

D2_8 = 0.4

License

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

Acknowledgments

We were inspired by several libraries in our methodology development and code development. We would like to especially thank their authors for the great work and publishing the code.

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