An efficient numerical algorithm was presented for discrete dislocation dynamics simulations in 2-dimensional finite polygonal domains. The algorithm was based upon a complex boundary integral equation method. By using the fast multipole method, linear complexity and storage requirements were met. Convergence studies showed that the algorithm was accurate, and numerically stable. The results for uniaxial load and bending moment load simulations under various loading rates were presented. The effect of finite size was studied, and the results showed that a higher loading rate gave less yielding and that a smaller specimen was harder than a larger one. This was in agreement with previous results, and demonstrated that the dislocation dynamics model could describe important features of a physical problem. The cut-off velocity (the maximum velocity of the dislocations) was an important model parameter. It was shown that a 4-times higher cut-off velocity, than that previously thought to be sufficient was required in order to obtain results that were independent of the cut-off velocity for bending-moment load simulations.

Discrete Dislocation Dynamics by an O(N) Algorithm. A.Jonsson: Computational Materials Science, 2003, 27[3], 271-88