A model of higher-order single crystal plasticity is presented and reviewed in order to develop a corresponding finite-element framework. Contrary to the underlying model of Gurtin [Int. J. Plast. 24:702-725, 2008], here rather than the slip rate, the slip and its gradient constitute primary micro state variables. The resulting rate-dependent formulation accounts for size effects through the free energy depending on density of geometrically necessary dislocations. The relationship to multifield theories of continua with microstructure is pointed out. With the presented finite-element approach, the corresponding fully coupled initial-boundary value problem is solved monolithically, and features of the model are illustrated in two preliminary numerical example
