Stochastic spatiotemporal analysis of 3D particle systems under shear and statistical validation of numerical DEM simulations

DFG优先方案1486的主要任务是了解粘性颗粒接近、接触和脱离过程中的物理化学(微)过程，并将这些知识应用于固体工艺工程中的产品设计。通过接触力学的知识，可以用数值方法确定系统中所有质点的空间位置、速度和加速度。因此，优先方案1486的第三个也是最后一个资助期的一个重要步骤是分析实验数据和确定微观和宏观性质之间的关系。通过对比真实实验和模拟实验得到的数据，可以验证DEM数值模拟及其接触模型。这样的验证然后允许系统地改变颗粒属性，目的是检测微观和宏观尺度之间的关系。在施密特教授小组提出的研究项目中，这些验证任务将借助基于时空模型的统计方法进行研究。随机分析和模型有助于从根本上降低实验(和时间分辨)3D图像数据的复杂性，并允许对实验图像数据进行有效的定量描述和评估，以及与数值结果进行统计比较。实际实验和数值模拟是由优先方案内的伙伴小组进行的，特别是由夸德教授、沃尔夫教授和奥恩哈默博士组成的小组。剪切试验的三维图像数据可以在不同的时间步长(分别为剪切角度)下获得。将从这种实验图像数据中提取颗粒、颗粒轨迹和接触网络，特别是对于非球形颗粒。使用自动算法，将在非均匀和各向异性(动态)接触网络中识别(关于粒子行为的)均匀区域。对于这些区域中的每一个，实验接触网络将使用随机分析进行定量描述。以数字方式获得的联系网络将通过统计检验来验证是否相等。为了实现这一点，我们将根据当前考虑的区域和粒子的属性(如粒子大小、形状和附着力)来描述粒子的“典型”行为。此外，接触网络将由随机图来建模，这使得我们能够在粒子系统级别上实现统计测试。

The main task of the DFG priority programme 1486 is to understand the physicochemical (micro-) processes during approach, contact and detachment of cohesive particles, and to implement this knowledge for product design in solids process engineering. By knowledge of contact mechanics it is possible to numerically determine spatial positions, velocities and accelerations of all particles in a system. Therefore, an important step during the third and last funding period of the priority programme 1486 is the analysis of experimental data and the identification of relationships between properties on the micro- and macro-scale. By comparison of data obtained from real and simulated experiments, numerical DEM simulations and their contact models can be validated. Such a validation then allows systematic variation of particle properties with the purpose to detect relationships between the micro- and macro-scale. In the proposed research project of the group of Prof. Schmidt, these validation tasks will be investigated with help of statistical approaches based on spatiotemporal models. Stochastic analyses and models help to essentially reduce the complexity of experimental (and time-resolved) 3D image data and permit an efficient quantitative description and evaluation of experimental image data as well as statistical comparisons with numerically obtained results. Real experiments and numerical simulations are performed by partner groups within the priority programme, particularly by the groups of Prof. Kwade, Prof. Wolf and Dr. Auernhammer. 3D image data of shear tests is available for various time steps (angles of shear, respectively). Particles, tracks of particles and contact networks will be extracted from such experimental image data, in particular also for non-spherical particles. Using automatic algorithms, homogeneous regions (with respect to particle behavior) will be identified in the inhomogeneous and anisotropic (dynamic) contact network. For each of these regions, the experimental contact network will be described quantitatively using stochastic analyses. Numerically obtained contact networks will be validated by statistical tests for equality. To make this possible, we will describe the "typical" behavior of particles in dependence of the currently considered region and the particle's properties like particle size, shape and adhesion. Furthermore, contact networks will be modeled by random graphs, which enables us to implement statistical tests on the level of particle systems.