The jump condition at a possibly non-material interface for geometrically-necessary dislocation density in field dislocation mechanics and its averaged approximation, phenomenological mesoscopic field dislocation mechanics, was derived. In the context of grain boundaries, the condition implied a tensorial constraint on all five grain boundary parameters, slip transmission at the boundary, possible grain boundary motion and dislocation nucleation/annihilation at the grain boundary. The jump condition was physically interpreted in special cases, and the importance of understanding dislocation motion at a boundary/interface as a flux across curves, and not surfaces, was emphasized.

Jump Condition for GND Evolution as a Constraint on Slip Transmission at Grain Boundaries. A.Acharya: Philosophical Magazine, 2007, 87[8-9], 1349-59