Gradient elasticity was used to treat straight screw and edge dislocations. Exact analytical solutions for the displacements, strain- and stress-fields and elastic energies were derived. These demonstrated the elimination of any singularity from the elastic fields and energies at the dislocation line. It was shown that the elastic stresses attained their maximum values at some distance (a/4) from the dislocation line.

Dislocations in the Theory of Gradient Elasticity. M.J.Gutkin, E.C.Aifantis: Scripta Materialia, 1999, 40[5], 559-66