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Signed distance field framework for unified DEM modeling of granular media with arbitrary particle shapes

Abstract

This paper presents a signed distance field (SDF) approach for unified discrete element method (DEM) modeling of granular media using arbitrarily shaped particles. The SDF approach employs a generic SDF-based interface defined by an SDF function and a surface projection function to rigorously model particle shapes and their ensuing complications on contact operations in DEM modeling. The signed distance is defined positive inside particles and negative when outside, and the zeroth isosurface of the SDF is conveniently used to represent the particle surface. The surface of a particle is discretized into a set of nodes. Node-to-surface algorithms are formulated to check the signs of the pertaining distance for contact detection. An energy-conserving contact theory is further employed to derive the contact interaction forces according to the contact potential defined on each intruding node. Based on the unified shape-contact description by SDF, specialised grain shape models are further developed to recover classical shape models as special cases, including poly-super-ellipsoid, poly-super-quadrics, spherical harmonics, polyhedron, and level set. A weighted spherical centroidal Voronoi tessellation-based numerical scheme is further developed for rigorous particle surface discretization and reconstruction. Demonstrative examples are presented to validate and showcase the capabilities of the proposed SDF approach for DEM modeling of granular media. The computational aspects, including the memory consumption and computational efficiency of the proposed approach for various particle models, are discussed.

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Acknowledgements

This work was financially supported by the Hong Kong Scholars Program (2020), the Research Grants Council of Hong Kong by GRF Project No. 16208720, the National Natural Science Foundation of China (51909289, 51978677, 11972030, 51909095, 5201101539, 52111530089), the Guangdong Basic and Applied Basic Research Foundation (2022A1515010848), the Shenzhen Science and Technology Project for Sustainable Development (KCXFZ202002011008532), the Shenzhen Natural Science Foundation (JCYJ20190807162401662), and the Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (HZQB-KCZYB-2020083).

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Lai, Z., Zhao, S., Zhao, J. et al. Signed distance field framework for unified DEM modeling of granular media with arbitrary particle shapes. Comput Mech 70, 763–783 (2022). https://doi.org/10.1007/s00466-022-02220-8

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  • DOI: https://doi.org/10.1007/s00466-022-02220-8

Keywords

  • Discrete element method
  • Arbitrary-shaped particle
  • Signed distance field
  • Contact potential
  • Spherical harmonics