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

The elastic field of complex 3-D dislocation ensembles is described by diff erential geometric representations, which allow computer simulations of mes oscopic plastic deformation without additional ad hoe approximations for sh ort-range dislocation reactions. The simple vector forms of differential ge ometry are independent of the coordinate system, and facilitate studies of dislocation generation, pileup formation, grain-boundary interaction, finit e-length dipole nucleation and break-up, junction nucleation and destructio n, interaction with defect clusters, and self-consistent boundary condition s. It is shown that the elastic field can be described in terms of simple c ombinations 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 t he only limitation being dislocation cores interpenetrating up to one Burge rs vector, a review of recent progress and examples of the aforementioned s hort- and long-range dislocation reactions are given, with particular empha sis on computational issues of space and time resolution.