Contact detection significantly affects the computational efficiency of discrete element simulations, especially for irregularly shaped elements. The dilated polyhedron is constructed by the Minkowski sum of a dilated sphere and a core convex polyhedron. One of the greatest advantages of using the dilated polyhedron in contact detection lies in its ability to be solved by calculating the nearest distance between corresponding core polyhedra. The approximate envelope function (AEF) of a dilated polyhedron is formed by the weighted summation of the second‐order dilated function of the polyhedral and spherical functions. The AEF can be used to represent the element in the optimization model for the contact center. Geometric calculations are then employed for the contact points on the core polyhedron, whereupon the contact detection is solved. The accuracy and stability of the proposed method by a 3‐D Voronoi tessellation are validated using analytical solutions and previously published simulation results. The efficiency tests show that the speedup of the CPU‐based multithread algorithm can reach 14 on a desktop. The direct shear test of the Voronoi shaped ballast is analyzed by this method. The shear stress under different vertical pressure is compared with previously published experimental and simulated results.

中文翻译：

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离散元法中带势函数的任意扩张多面体接触检测的新方法

接触检测会显着影响离散元素模拟的计算效率，尤其是对于形状不规则的元素。膨胀多面体由膨胀球和核心凸多面体的Minkowski总和构成。在接触检测中使用膨胀多面体的最大优势之一在于其能力，可以通过计算相应的核心多面体之间的最近距离来解决。扩张多面体的近似包络函数（AEF）由多面体和球形函数的二阶扩张函数的加权总和形成。AEF可用于表示联系中心优化模型中的元素。然后对核心多面体上的接触点进行几何计算，从而解决了接触检测问题。使用解析解决方案和先前发表的仿真结果验证了3维Voronoi镶嵌方法对所提方法的准确性和稳定性。效率测试表明，基于CPU的多线程算法在台式机上的加速可以达到14。通过这种方法分析了Voronoi形压载物的直接剪切试验。将不同垂直压力下的剪应力与先前发表的实验和模拟结果进行了比较。