An efficient and minimalist scheme for continuum dislocation dynamics

Alireza Kalaei, Yang Xiang, and Alfonso H.W. Ngan, Int. J. Plast. 158, 103433 (2022).


Continuum dislocation dynamics methods have received considerable interests for simulating dislocation microstructures at the meso-scale, serving as potential tools for bridging the gap between micro- and macro-scale models for the plastic behaviours of crystalline materials. Recently, an exact evolution equation for the “all-dislocation” density that represents dislocation quantities over both space and dislocation-character domains has been developed by one of the present authors. The “all-dislocation” representation is superior to representations based on the Nye tensor or geometrically necessary dislocations (GND), since the statistically stored dislocation (SSD) contents will be preserved. In this paper, a numerical scheme is presented to solve the dynamics of the “all-dislocation” density efficiently, with long-range elastic interaction between dislocations accounted for via Mura's formula after singularity removal. The proposed simulation scheme is demonstrated by simulation examples in the multi-scale hierarchy, from intensive microstructures of individual dislocations including Frank-Read source and Orowan looping, to extensive micro-structures of coarse-grained dislocation densities in single- and multi-slip in the face-centred cubic crystal structure.


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