Stochastic particle models for the quantification of relationships between structural characteristics and mechanical properties to predict particle breakage behaviour

在提议的项目中，我们开发参数化材料模型，定量捕获分散结构特征和机械性能之间的依赖关系。这些模型取决于材料的性质，并推广了H. Rumpf的性质函数。这种方法的目的是估计影响断裂行为的材料相关参数，同时必须分离工艺相关应力的影响。在此基础上，推导了断裂概率和断裂函数。此外，为了使结果可用于spp1679的其他项目，这些都被实现到软件框架内的断裂模块中。为了系统地研究材料特性和团聚体结构特征对其力学行为的影响，使用随机粒子模型生成3D微观结构，然后将其用作DEM模拟的输入。DEM模拟是与Heinrich教授的工作组合作进行的。随机粒子模型有助于生成具有给定结构特征的定制微结构。因为可以根据需要模拟任意数量的实现，所以这是生成足够大的数据库以进行统计推断的理想工具。对各种团块的三维图像数据进行结构分割，保证了所研究的微观结构的真实感。在第一个资助期，我们分析了压缩正常载荷下团聚体的力学行为。第一篇联合文章已经提交，其中主要颗粒的大小分布的影响进行了探讨。在第二个资助期，将研究动态载荷下的行为，并将结果用于描述颗粒破碎。参数化材料模型，或者更准确地说，在这些模型中捕获的分散特性，被相应地选择。用于固体聚合描述的材料模型由参数多元概率分布指定，该分布是基于所谓的copula构建的。这种方法使我们能够同时捕获各种分散特性，例如，颗粒大小，颗粒形状，内部孔隙度，以及诸如断裂能量等机械特性。因此，力学性能可以通过评估条件分布来预测。基于模型的破碎概率和破碎函数的描述结合了这些结果以及给定的（依赖于过程的）颗粒应力。这提供了在其设备/工艺描述中考虑颗粒破碎的合作伙伴组的链接。我们将与Z项目合作，指定并实现一个适用于spp1679中开发的软件系统的“破碎模块”。

In the proposed project we develop parametric material models that quantitatively capture dependencies between disperse structural characteristics and mechanical properties. These models depend on the material properties and generalize the property function by H. Rumpf. The aim of this approach is to estimate the material-dependent parameters that influence breakage behaviour, while the effect of process-dependent stress has to be separated. Based on these data, breakage probabilities and breakage functions are derived. Furthermore, these are implemented into a breakage module inside the software framework in order to make the results available for other projects of the SPP 1679.For systematic investigations of the effect of material properties and structural characteristics of agglomerates on their mechanical behaviour, a stochastic particle model is used to generate 3D microstructures, which are then used as input to DEM simulations. DEM simulations are performed in cooperation with the work group of Prof. Heinrich. The stochastic particle model facilitates the generation of tailored microstructures with given structural characteristics. Because as many realizations as needed can be simulated, this is an ideal tool to generate a database large enough for statistical inference. Structural segmentation of 3D image data of various agglomerates ensures that the microstructures under investigation are realistic. In the first funding period, we analyse the mechanical behaviour of agglomerates under compressive normal load. A first joint article has been submitted where the effect of the size distribution of primary particles is explored. In the second funding period, the behaviour under dynamical load will be studied and the results will be used to describe particle breakage. The parametric material models, or more precisely, the disperse properties captured in these models, are chosen accordingly. The material models for the aggregated description of solids are specified by parametric multivariate probability distributions, which are constructed based on so-called copulas. This approach allows us to capture various disperse properties simultaneously, e.g., particle size, particle shape, inner porosity, together with mechanical properties like e.g. breakage energies. Therefore, mechanical properties can be predicted by evaluating conditional distributions. The model-based description of breakage probabilities and breakage functions incorporates these results as well as the given (process-dependent) particle stress. This provides the link to the partner groups that consider particle breakage in their apparatus/process descriptions. In cooperation with the Z project, we will specify and implement a "breakage module" suitable for the software system developed in the SPP 1679.