A hierarchical, spherical harmonic-based approach to simulate abradable, irregularly shaped particles in DEM

A novel approach is presented for simulating non-spherical particles in the discrete element method (DEM). A particle's shape is described through a hierarchy of representations using spherical harmonic expansions. The expansion is computed at nodes, obtained by discretising the particle’s surface. A low-degree expansion, i.e., one containing few terms, is sufficient to approximate a particle's overall shape without any surface texture. Expansions are computed to high degrees only at interparticle contacts, rather than for the entire particle, which reduces the computational cost. The advantages of this approach include the ability to simulate a wide range of particle shapes and adaptive resolution depending on spatial and temporal considerations. An additional unique benefit is that changes of particle shape due to chipping can be captured in DEM for the first time. This is accomplished by progressively omitting more of the highest-degree terms from the expansion to give an increasingly smooth surface.