  The stress fields of dislocations predicted by classical elasticity are known
to be unrealistically large approaching the dislocation core, due to the
singular nature of the theory. While in many cases this is remedied with the
approximation of an effective core radius, inside which ad hoc regularizations
are implemented, such approximations lead to a compromise in the accuracy of
the calculations. In this work, an anisotropic non-singular elastic
representation of dislocation fields is developed to accurately represent the
near-core stresses of dislocations in $\alpha$-iron. The regularized stress
field is enabled through the use of a non-singular Green's tensor function of
Helmholtz-type gradient anisotropic elasticity, which requires only a single
characteristic length parameter in addition to the material's elastic
constants. Using a novel magnetic bond-order potential to model atomic
interactions in iron, molecular statics calculations are performed, and an
optimization procedure is developed to extract the required length parameter.
Results show the method can accurately replicate the magnitude and decay of the
near-core dislocation stresses even for atoms belonging to the core itself.
Comparisons with the singular isotropic and anisotropic theories show the
non-singular anisotropic theory leads to a substantially more accurate
representation of the stresses of both screw and edge dislocations near the
core, in some cases showing improvements in accuracy of up to an order of
magnitude. The spatial extent of the region in which the singular and
non-singular stress differ substantially is also discussed. The general
procedure we describe may in principle be applied to accurately model the
near-core dislocation stresses of any arbitrarily shaped dislocation in
anisotropic cubic media.
