Depending on the appropriate scale, modelling of dislocations may require a discrete or a continuous formalism.
When the plastic behaviour is mostly controlled by dislocation interplay at a scale far beyond the mean dislocation spacing, individual dislocations can no longer be resolved and a continuous formulation is required. The talk address this situation.
We present a rigorous formulation of the transition between the discrete, where plastic flow is resolved at the scale of individual dislocations, and the continuum, where dislocations are represented by densities. We show that the required coarse-graining procedure generates scale-dependant stresses that act as friction or back stresses. We also show that these correlation-induced stresses contain symmetry-breaking components that generate Peach-Koehler forces that are independent on the sign of the Burgers vector.
Finally, we show that one of the correlation-induced stresses (a symmetry-breaking back stress) plays a dominant role in the emergence of large-scale dislocation patterns.