A framework was presented for carrying out finite deformation discrete dislocation plasticity calculations. The discrete dislocations were presumed to be adequately represented by the singular linear elastic fields so that the large deformations near dislocation cores were not modeled. The finite deformation effects which were accounted for were finite lattice rotations, and shape changes due to slip. As a consequence of the non-linearity, an iterative procedure was needed to solve boundary value problems. Elastic anisotropy together with lattice curvature was shown to lead to a polarization stress term in the rate boundary value problem. The general three-dimensional framework was specialized to plane strain. The plane strain specialization was implemented in a conventional finite element code and two numerical examples were given: plane strain tension of a single crystal strip and combined bending and tension of that strip. The capabilities and limitations of a conventional finite element framework for this class of problems were illustrated.

Finite Strain Discrete Dislocation Plasticity. V.S.Deshpande, A.Needleman, E.Van der Giessen: Journal of the Mechanics and Physics of Solids, 2003, 51[11-12], 2057-83