A special gradient theory of elasticity was used to analyse dislocations and disclinations, with emphasis being placed on the elimination of strain singularities which appeared in the classical theory of elasticity. In the case of disclinations, non-singular expressions were derived for the elastic strains. This demonstrated that dipoles of straight disclinations of general type gave zero or finite values for the strain components at the disclination line. The finite values depended strongly upon the dipole arm, and exhibited a regular monotonic (wedge disclinations) or non-monotonic (twist disclinations) behavior for short-range interactions. At annihilation distances, the elastic strains tended smoothly to zero. The gradient and classical solutions coincided far from the disclination line. When the dipole arm was much smaller than the scale unit, the elastic fields of a dipole of wedge disclinations transformed into the elastic field of an edge dislocation, as in the case of classical elasticity.

Dislocations and Disclinations in Gradient Elasticity. M.Y.Gutkin, E.C.Aifantis: Physica Status Solidi B, 1999, 214[2], 245-84