Non-singular solutions for dislocation and disclination fields had recently been obtained by using a robust model of gradient elasticity theory. These solutions, whose form was simple and easy to implement, were obtained by reducing the gradient elasticity problem to a corresponding linear elasticity boundary value problem through the solutions of an inhomogeneous Helmholtz equation where the source term was the classical singular solution. The Laplacian in the Helmholtz equation, involving the extra gradient coefficient, produces a new term in the gradient solution which asymptotically approaches the negative of the classical elasticity solution on the dislocation line. Thus, the singularity was eliminated and an arbitrary estimate of the dislocation core size introduced in classical theory, was not required. These predictions were tested against atomistic calculations and their implications to various dislocation related configurations were discussed. Due to the simple and elegant form of these solutions, it was hoped that they will be useful in discrete dislocation dynamics simulations.

Non-Singular Dislocation Fields. E.C.Aifantis: IOP Conference Series - Materials Science and Engineering, 2009, 3[1], 012026