Multi-superquadric and Poly-superquadric DEM Models

The superquadric equation is a general method for describing spherical and irregular particles in a mathematical sense, and this equation can be used to construct particle morphologies with different surface sharpness and aspect ratio. However, the particles constructed by the superquadric equation are geometrically symmetric and strictly convex, which is different from the actual particle shape and limits the further engineering application of the superquadric model. In recent years, the non-spherical discrete element method based on the combined particle method has been widely developed and applied. Tetrahedral particles are formed by combining several spheres, and local cluster structures are randomly distributed in granular materials (Zhao et al. in Soft Matter 15:2260–2268, 2019). Considering the geometric symmetry of the ellipsoid element, one-eighth of the eight ellipsoids are spliced together to form a poly-ellipsoid with a smooth surface.