An implicit iterative finite element scheme was developed for the strain gradient theory of single-crystal plasticity that accounted for the self-energy of geometrically necessary dislocations. This strain-gradient theory belongs to the Gurtin framework for viscoplastic single-crystals. The self-energy of geometrically necessary dislocations gave a specific form of energetic higher-order stresses. An implicit finite element equation was obtained for solving a set of homogenization equations. The developed scheme was employed to analyze a model grain, and was verified by comparison with the analytical estimation derived by Ohno and Okumura (2007). The computational efficiency of the scheme and the incremental stability were discussed. Furthermore, it was shown that the developed scheme was available and applicable to different types of higher-order stresses including energetic and dissipative terms.

Implicit Iterative Finite Element Scheme for a Strain Gradient Crystal Plasticity Model Based on Self-Energy of Geometrically Necessary Dislocations. R.Kametani, K.Kodera, D.Okumura, N.Ohno: Computational Materials Science, 2012, 53[1], 53-9