The higher-dimensional kinematical dislocation continuum theory of Hochrainer (2006) and a homogenized version thereof by Hochrainer, Zaiser and Gumbsch (2010) were reviewed. A three-dimensional finite element solution of the homogenized theory was presented, interpreted physically and compared to the results of geometrically necessary dislocation theory.

Dislocation Transport in Single Crystals and Dislocation-Based Micromechanical Hardening. S.Wulfinghoff, V.Glavas, T.Böhlke: Proceedings in Applied Mathematics and Mechanics, 2011, 11[1], 449–50