The superquadric function is employed to represent spherical and non-spherical particles. Although particles with different aspect ratios and surface blockiness can be described using the superquadric equation, the shapes of these particles are geometrically symmetric and further engineering applications are limited. In this work, a poly-superquadric element based on the superquadric function is developed. This model is composed of eight one-eighth superquadric elements and is used to represent superquadric elements, poly-ellipsoids, and asymmetrically shaped particles. To examine the validity of the poly-superquadric DEM model, the numerical results of a hemisphere impacting a plane are obtained and compared with the theoretical results. Then, the mass flow rates of particles of different shapes are investigated. The results show that the spheres have the fastest flow rate, and the flow rate of the pebble-shaped particles constructed by the poly-superquadric elements is faster than that of the cube-like particles. Moreover, the flow rate of superquadric and poly-superquadric elements decreases as the blockiness parameter increases. Geometrically asymmetric and elongated particles are rearranged to form interlocking and local clusters, which limit the relative motion between particles and reduce the flowability of non-spherical granular materials.

超二次函数用于表示球形和非球形粒子。尽管可以使用超二次方程描述具有不同纵横比和表面块度的粒子，但这些粒子的形状是几何对称的，进一步的工程应用受到限制。在这项工作中，开发了一种基于超二次函数的多超二次元。该模型由八个八分之一的超二次元组成，用于表示超二次元、多椭球和不对称形状的粒子。为了检验多超二次曲面 DEM 模型的有效性，获得了半球撞击平面的数值结果，并与理论结果进行了比较。然后，研究了不同形状颗粒的质量流量。结果表明，球体的流速最快，由多超二次元构成的卵石形颗粒的流速比立方体颗粒的流速快。此外，随着块度参数的增加，超二次曲面和多超二次曲面单元的流速降低。几何不对称和细长的颗粒重新排列形成互锁和局部簇，限制了颗粒之间的相对运动并降低了非球形颗粒材料的流动性。