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

DFG优先计划1486的主要任务是了解物理化学（微）过程中的方法，接触和分离的粘性颗粒，并实施这些知识的产品设计在固体工艺工程。通过接触力学的知识，可以用数值方法确定系统中所有粒子的空间位置、速度和加速度。因此，在优先计划1486的第三个也是最后一个供资期内的一个重要步骤是分析实验数据，并确定微观和宏观尺度上的性质之间的关系。通过比较真实的试验数据和模拟试验数据，验证了数值离散元模拟及其接触模型的正确性。这样的验证，然后允许系统变化的颗粒特性的目的，以检测微观和宏观尺度之间的关系。在施密特教授小组的拟议研究项目中，将借助基于时空模型的统计方法对这些验证任务进行研究。随机分析和模型有助于从根本上降低实验（和时间分辨）的三维图像数据的复杂性，并允许有效的定量描述和评价实验图像数据，以及与数值获得的结果进行统计比较。优先方案内的伙伴小组，特别是Kwade教授、Wolf教授和Auernhammer博士小组进行了真实的实验和数值模拟。剪切试验的3D图像数据可用于各种时间步长（分别为剪切角）。将从这样的实验图像数据中提取颗粒、颗粒的轨迹和接触网络，特别是还针对非球形颗粒。使用自动算法，将在非均匀和各向异性（动态）接触网络中识别均匀区域（相对于粒子行为）。对于这些区域中的每一个，将使用随机分析定量地描述实验接触网络。数值获得的接触网络将通过相等性的统计检验进行验证。为了使这成为可能，我们将描述依赖于当前考虑的区域和颗粒的属性（如颗粒大小，形状和粘附力）的颗粒的“典型”行为。此外，接触网络将由随机图建模，这使我们能够实现粒子系统水平上的统计测试。

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.