We present a continuum model for the dynamics of dislocation arrays. The continuum model is derived rigorously from the discrete dislocation dynamics model using asymptotic analysis. The obtained continuum model contains an integral over the dislocation array surface representing the long-range interaction of dislocations, and a local term that comes from the line tension effect of dislocations. The size-dependent effect due to dislocation line tension is accurately incorporated. We also present numerical simulations using this continuum model including applications to dislocation structures of low angle grain boundaries.
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