A time step must be selected for any explicit discrete element method (DEM) simulation. This time step must be small enough to ensure a stable simulation but should not be overly conservative for computational efficiency. There are established methods to estimate critical time steps for simulations of spherical particles. However, there is a comparable lack of guidance on choosing time steps for DEM simulations involving nonspherical particles: a fact which is increasingly problematic as simulations of nonspherical particles become more commonplace. In this article, the eigenvalues of the amplification matrix are used to develop an explicit formula for the critical time step for a range of shapes including ellipsoids, convex superquadrics and convex, central symmetric polyhedra. This derivation is based on a linear analysis and applies to both underdamped and overdamped systems. The dependence on the particle mass and contact stiffness expected for a system of spheres is recovered. For a fixed particle mass, as particle shape becomes increasingly nonspherical, the critical time step decreases nonlinearly. Thus, estimating a critical time step by assuming a sphere of equivalent volume may not always be conservative.

中文翻译：

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中心对称凸粒子离散元方法模拟的关键时间步

任何显式离散元素方法（DEM）模拟都必须选择一个时间步。该时间步长必须足够小以确保稳定的仿真，但对于计算效率不应过于保守。已经建立了估算关键时间步长的方法，以模拟球形颗粒。但是，在选择涉及非球形粒子的DEM模拟的时间步骤时，缺乏类似的指导：随着非球形粒子的模拟变得越来越普遍，这一事实变得越来越成问题。在本文中，将放大矩阵的特征值用于为包括椭圆体，凸超二次曲面和凸，中心对称多面体在内的各种形状的临界时间步长开发明确的公式。此推导基于线性分析，适用于欠阻尼和过阻尼系统。恢复了对球体系统预期的颗粒质量和接触刚度的依赖性。对于固定的粒子质量，随着粒子形状变得越来越非球形，临界时间步长将非线性减小。因此，通过假设等效体积的球体来估计关键时间步长可能并不总是保守的。