Data-mining of dislocation microstructures: concepts for coarse-graining of internal energies

TL;DR

This paper introduces a systematic data-mining method to extract energy densities from dislocation microstructures, enabling better continuum modeling of dislocation plasticity by addressing voxel-size dependence issues.

Contribution

A novel coarse-graining approach that derives energy density formulations from discrete dislocation data, improving continuum dislocation models.

Findings

Successfully extracts energy densities from microstructure data

Addresses voxel-size dependence in energy calculations

Applicable to 2D and 3D dislocation simulations

Abstract

Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such information from reference simulations, such as discrete dislocation dynamics or molecular dynamics. Here, a novel data-mining approach is proposed through which energy density data from systems of discrete dislocations can be extracted. Our approach relies on a systematic and controlled coarse-graining process and thereby is consistent with the length scale of interest. For data-mining, a range of different dislocation microstructures that were generated from 2D and 3D discrete dislocation dynamics simulations, are used. The analyses of the data sets result in energy density formulations as function of various dislocation density fields. The proposed approach solves the long-standing problem of voxel-size dependent energy calculation during coarse graining of dislocation microstructures. Thus, it is crucial for any continuum dislocation dynamics simulation.