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The stress fields of dislocations predicted by classical elasticity are knownto be unrealistically large approaching the dislocation core, due to thesingular nature of the theory. While in many cases this is remedied with theapproximation of an effective core radius, inside which ad hoc regularizationsare implemented, such approximations lead to a compromise in the accuracy ofthe calculations. In this work, an anisotropic non-singular elasticrepresentation of dislocation fields is developed to accurately represent thenear-core stresses of dislocations in $\alpha$-iron. The regularized stressfield is enabled through the use of a non-singular Green's tensor function ofHelmholtz-type gradient anisotropic elasticity, which requires only a singlecharacteristic length parameter in addition to the material's elasticconstants. Using a novel magnetic bond-order potential to model atomicinteractions in iron, molecular statics calculations are performed, and anoptimization procedure is developed to extract the required length parameter.Results show the method can accurately replicate the magnitude and decay of thenear-core dislocation stresses even for atoms belonging to the core itself.Comparisons with the singular isotropic and anisotropic theories show thenon-singular anisotropic theory leads to a substantially more accuraterepresentation of the stresses of both screw and edge dislocations near thecore, in some cases showing improvements in accuracy of up to an order ofmagnitude. The spatial extent of the region in which the singular andnon-singular stress differ substantially is also discussed. The generalprocedure we describe may in principle be applied to accurately model thenear-core dislocation stresses of any arbitrarily shaped dislocation inanisotropic cubic media.

Atomistically enabled nonsingular anisotropic elastic representation of near-core dislocation stress fields in $\alpha$-iron