Dislocations and disclinations in the gradient theory of elasticity

The results of application of gradient theory of elasticity to a descriptio n of elastic fields and dislocation and disclination energies are considere d. The main achievement made in this approach is the removal of the classic al singularities at defect lines and the possibility of describing short-ra nge interactions between them on a nanoscopic level. Non-singular solutions for stress and strain fields of straight disclination dipoles in an infini te isotropic medium have been obtained within a version of the gradient the ory of elasticity. A description is given of elastic fields near disclinati on lines and of specific features in the short-range interactions between d isclinations, whose study is impossible to make in terms of the classical l inear theory of elasticity. The strains and stresses at disclination lines are shown to depend strongly on the dipole arm d. For short-range interacti on between disclinations, where d varies from zero to a few atomic spacings , these quantities vary monotonically for wedge disclinations and nonmonoto nically in the case of twist disclinations, and tend uniformly to zero as d isclinations annihilate. At distances from disclination lines above a few a tomic spacings, the gradient and classical solutions coincide. As in the cl assical theory of elasticity, the gradient solution for the wedge-disclinat ion dipole transforms to the well-known gradient solution for a wedge dislo cation at distances d substantially smaller than the interatomic spacing. ( C) 1999 American Institute of Physics. [S1063-7834(99)01112-0].