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

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.

Automated summary

This paper presents a signed distance field approach for DEM modeling of granular media with arbitrarily shaped particles. The approach uses a generic SDF-based interface to rigorously model particle shapes and their contact operations. It defines the signed distance inside and outside particles and represents the particle surface using the zeroth isosurface of the SDF. The paper also develops specialized grain shape models and a numerical scheme for particle surface discretization and reconstruction. Demonstrative examples validate the proposed approach and computational aspects are discussed.