Computer simulations of mesoscopic plastic deformation with differential geometric forms for the elastic field of parametric dislocations : Review of recent progress

Abstract
The elastic field of complex 3-D dislocation ensembles is described by differential geometric representations, which allow computer simulations of mesoscopic plastic deformation without additional ad hoc approximations for short-range dislocation reactions. The simple vector forms of differential geometry are independent of the coordinate system, and facilitate studies of dislocation generation, pileup formation, grain-boundary interaction, finite-length dipole nucleation and break-up, junction nucleation and destruction, interaction with defect clusters, and self-consistent boundary conditions. It is shown that the elastic field can be described in terms of simple combinations of three basic vectors and their dyadics in real and reciprocal space. These vectors are the unit tangent, Burgers vector, and unit radial vector between a source point on the dislocation and a field point. With the only limitation being dislocation cores interpenetrating up to one Burgers vector, a review of recent progress and examples of the aforementioned short- and long-range dislocation reactions are given, with particular emphasis on computational issues of space and time resolution.