A hierarchical multi-scale model was presented that coupled a region of material described by discrete dislocation plasticity to a surrounding region described by conventional crystal plasticity. The coupled model was aimed at capturing non-classical plasticity effects such as the long-range stresses associated with a density of geometrically necessary dislocations and source limited plasticity, while also accounting for plastic flow and the associated energy dissipation at much larger scales where such non-classical effects were absent. The key to the model was the treatment of the interface between the discrete and continuum regions, where continuity of tractions and displacements was maintained in an average sense and the flow of net Burgers vector was managed via “passing” of discrete dislocations. The formulation was used to analyze two plane strain problems: (i) tension of a block and (ii) crack growth under mode I loading with various sizes of the discrete dislocation plasticity region surrounding the crack tip. The computed crack growth resistance curves were nearly independent of the size of the discrete dislocation plasticity region for region sizes ranging from 30μ x 30μ to 10μ x 5μ. The multi-scale model could reduce the computational time for the mode I crack analysis by a factor of 14 with little or no loss of fidelity in the crack growth predictions.

Multi-Scale Plasticity Modelling: Coupled Discrete Dislocation and Continuum Crystal Plasticity. M.Wallin, W.A.Curtin, M.Ristinmaa, A.Needleman: Journal of the Mechanics and Physics of Solids, 2008, 56[11], 3167-80