凹形多面体离散单元的水平集函数接触算法

多面体模型理论上可构造任意颗粒形态,然而受单元接触算法的限制,仅用于凸形颗粒材料的离散元模拟。对于具有凹形特征的多面体单元,单个接触点的搜索算法难以精确计算单元间的作用力。考虑多面体单元间存在单个或多个接触点的计算特性,本文发展了适用于凸形和凹形多面体颗粒材料的水平集函数接触算法。该方法通过点-三角形单元距离计算方法和奇-偶数判定方法建立多面体单元的零水平集函数和空间水平集函数,并对水平集函数进行三线性插值,可得到多面体单元间的单个或多个接触点。为检验水平集函数接触算法的可靠性,对球形和凹形多面体颗粒材料的堆积和倒塌过程进行离散元模拟,并分析颗粒形状对堆积密度和休止角的影响规律。

Level set contact algorithm for DEM simulations of concave polyhedron elements

The polyhedral model can theoretically be used to construct arbitrarily shaped particles in the discrete element method (DEM).Due to the limitations of the DEM contact algorithm,the polyhedral model is only used to simulate the dynamic properties of particles with convex morphology.For polyhedral elements with concave surfaces,the contact algorithm for individual contact points can not accurately calculate the forces between elements.To accurately calculate single or multiple contact points between polyhedral particles,a level-set contact algorithm is developed for convex and concave polyhedral elements.In this method,the spatial level-set function and zero level-set function of the polyhedral element are established by the point-triangle element distance calculation method and the odd-even judgment method,and single or multiple contact points between polyhedral elements are obtained by solving the two level-set functions.To examine the reliability of the level-set contact algorithm,the packing and collapse processes of spherical and concave polyhedral granular materials are simulated using the DEM.Meanwhile,the effects of particles shapes on the volume fraction and angle of repose are analyzed.