Non-singular dislocation fields

Non-singular solutions for dislocation and disclination fields have recently been obtained by the author and his co-workers by using a robust model of gradient elasticity theory. These solutions, whose form is simple and easy to implement, are 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 is 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 is eliminated and an arbitrary estimate of the dislocation core size introduced in classical theory, is not required. These predictions are tested against atomistic calculations and their implications to various dislocation related configurations are discussed. Due to the simple and elegant form of these solutions, it is hoped that they will be useful in discrete dislocation dynamics simulations.