  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.
