Homogenization of the elementary shears produced by dislocations was considered within the framework of a discrete continuum numerical model. Here, a dislocation dynamics simulation was substituted for the constitutive form which was normally used

in finite-element calculations. As an example of the discrete continuum model, the stress field of a single dislocation was obtained as a solution of the boundary value problem. This method was shown to be able to account for size effects which arose from line tension effects and stress concentrations at the tips of dislocation pile-ups.

Homogenization Method for a Discrete-Continuum Simulation of Dislocation Dynamics. C.Lemarchand, B.Devincre, L.P.Kubin: Journal of the Mechanics and Physics of Solids, 2001, 49[9], 1969-82