Linking different scales: discrete, self-consistent field, and stochastic dislocation dynamics

The dynamics behavior of an assembly of parallel dislocations is investigated at different length scales. In the first part, it is shown that a discrete dislocation system is able to reproduce several important features of plastic deformation. Then, a self-consistent field continuum model is derived. Finally, a stochastic approach is outlined, which can be considered as an intermediate scale description between the discrete and the continuum models.