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

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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.