Stochastic nature of granular particle interaction and its influence on the system dynamics

对粒子相互作用的充分描述是理解颗粒系统动力学的必要前提，因此也是定量正确(预测)模拟的必要前提。工业规模的粒子系统在大多数情况下由非常大量的粒子组成，这些粒子又以一种复杂的方式相互作用，这主要是因为它们的复杂形状和表面性质。因此，对于粒子系统的模拟，我们必须在足够数量的粒子和对粒子相互作用的充分描述之间进行折衷：尽管经常使用的球形粒子模型允许模拟数千个粒子，但该模型肯定过度简化了真实的锐边粒子的相互作用。另一方面，虽然在原则上是可能的，但对单个颗粒及其复杂相互作用的高度复杂的建模只能在短时间内对小系统进行模拟，即使在非常强大的计算机上也是如此。本研究项目旨在解决粒子相互作用的随机建模问题，它在统计意义上反映了粒子的复杂几何形状(导致复杂的相互作用)。如果成功，这种类型的建模将把球形粒子模拟的计算效率与更复杂的粒子和粒子相互作用模型提供的粒子相互作用的真实描述结合起来。在第一个资助期，研究集中在法向粒子相互作用上。作为主要结果，我们导出了粒子几何和表面纹理到法向恢复系数波动系数的随机特性的映射，该映射可用于高效的事件驱动粒子模拟。此外，我们还推导了可用于时步算法(DEM)的法向粒子相互作用的脉动相互作用力方案。颗粒系统动力学的完整描述还需要决定粒子切向相互作用的量的知识，即切向恢复系数(对于事件驱动模拟)和作用力的切向分量(对于DEM模拟)。从颗粒的几何形状属性及其表面属性推导出这些量将是本提案的主题。此外，我们的目标也是计算强非球形粒子的两个分量(法向和切向)。因此，我们的目标是分别通过随机恢复系数(法向和切向)或随机力来完整地描述颗粒颗粒之间的相互作用。这些特征将被用来通过简单的技术相关系统来检验随机描述方法。

The adequate description of particle interaction is a necessary prerequisite for the understanding of the dynamics of granular systems and, thus, for quantitatively correct (predictive) simulations. Particle systems of industrial scale consist in most cases of a very large number of particles which in turn interact in a complicated way, mainly because of their complex shape and their surface properties. Therefore, for the simulation of particle systems we have to compromize between an adequate number of particles and an adequate description of the grains' interaction: While the frequently applied model of spherical particles allows for the simulation of many thousand grains, this model certainly oversimplifies the interaction of realistic sharply edged particles. On the other hand, while possible in principle, highly sophisticated modeling of single grains and their complex interaction can be simulated only for small systems over short real times, even on very powerful computers. The present research project seeks a solution of the problem in stochastic modeling of the particle interaction which reflects the complex geometry of the particles (leading to complex interaction) in a statistical sense. If successful, this type of modeling will combine the computational efficiency of the simulation of spherical particles with the realistic description of particle interaction provided by more complex particle and particle interaction models.In the first funding period the research was focused on the particle interaction in normal direction. As main results we a) derived a mapping of particle geometry and surface texture to the stochastic properties of a fluctuating coefficient of normal restitution which may be used for highly efficient event-driven particle simulations. Moreover, b) we derived a fluctuating interaction force scheme for particle interaction in normal direction which can be used in time-stepping algorithms (DEM).The complete description of granular system dynamics requires also the knowledge of the quantities determining the tangential interaction of particles, that is, the coefficient of tangential restitution (for event-driven simulations) and the tangential component of the interaction force (for DEM simulations). The derivation of these quantities from the geometric shape properties of the particles and their surface properties will be subject of the present proposal. Moreover, we aim also to compute both components (normal and tangential) for particles whose shape is strongly non-spherical. Thus, we aim to a complete description of the interaction of granular particles by means of stochastic coefficients of restitution (normal and tangential) or stochastic forces, respectively. These characteristics shall be used to test the method of stochastic description by means of simple, however, technical relevant systems.