Characterization, Modelling, and Homogenization of Dislocation Networks Using Interpretable Data Analysis

该项目的目标是用新的、专门的数据分析方法来识别和制定晶体材料中位错网络随时间演变的物理相关性。调查是基于离散位错动力学（DDD）模拟的数据。到目前为止，很大程度上是未知的措施，表征位错网络，以及如何物理描述可能看起来像。DDD模拟有两个优点。(i)它们有助于观察三维网络结构，并允许了解材料中的微观结构变化。DDD模拟产生的数据包含集体位错运动的基础上的基本物理关系的现象。人们也可以在真实的材料中观察到这些现象。然而，目前尚不清楚这些现象与环境参数和材料结构的影响之间的因果关系。这使得制定关于宏观调查和真实的系统的模拟的进一步发展和使用的假设困难。(ii)DDD数据的表征有利于位错系统在空间范围上的可扩展性分析。以前的位错网络均匀化方法仅限于简化系统或太不准确，无法再现DDD模拟中观察到的机制。因此，它们无法取代昂贵的DDD模拟。我们的研究目标之一是从DDD数据中学习均匀化状态的演化，并推导出均匀化公式。我们假设，均匀化位错网络的演变可以通过依赖于从数据中学习的模型的帮助下的物理相关性的深刻知识，以显着更高的准确性和物理严谨性来描述。

The objective of this project is the identification and formulation of physical correlations in the temporal evolution of dislocation networks in crystalline materials with new, specialized data-analysis methods. The investigations are based on data from discrete dislocation dynamics (DDD) simulations. Up to now, it is largely unknown which measures characterize dislocation networks, and how a physical description might look like. DDD simulations come with two advantages. (i) They facilitate observing network structures in three dimensions and allow for an understanding of the microstructural changes in the material. DDD simulations produce data that contain phenomena of collective dislocation motion based on fundamental physical relations. One can observe these phenomena in real materials as well. However, the causal connections of these phenomena and the impact of environmental parameters and of the material structure currently are unclear. This makes formulating hypotheses regarding the further development and the use of simulations for macroscopic investigations and real systems difficult. (ii) A characterization of DDD data facilitates scalable analyses of dislocation systems in terms of the spatial extent.Previous approaches for the homogenization of dislocation networks are restricted to simplified systems or are too inaccurate to reproduce the mechanisms observed in DDD simulations. So they cannot replace costly DDD simulations. One of our research objectives is to learn the evolution of homogenized states from the DDD data and to derive a homogenized formulation. We assume that the evolution of homogenized dislocation networks can be described with significantly higher accuracy and physical rigor by relying on profound knowledge of the physical correlations with the help of models learned from data.