Invited Lecture
A Phase Field approach to describe the collective properties of dislocations

The plastic properties of crystalline materials are determined by the collective evolution of the dislocation network. A possible approach to follow the 
 complex evolution of  a dislocation ensemble is discreet dislocation dynamic simulation but it is a computationally rather demanding task.  For many
 problems another approach is to describe the dislocation network with continuous fields like the statistically stored dislocation density,  the geometrically
 necessary dislocation density, etc. Certainly a key issue here is how to set up the appropriate time evolution equations for the fields introduced. An 
effective approach applied in several field in physics is the phase field method. It requires a scalar functional of the different fields that is minimized in 
equilibrium, and appropriate mobility functions determining the dynamics of the system.

For a system of edge dislocations a phase field functional is proposed that is directly derived from the microscopic properties of dislocations. It is show
 that due to the constrained motion of the dislocations the phase field theory of dislocation density evolution has an unusual character  compared to other
 phase field theories. It is explained how this specific feature leads to dislocation patterning. 

In the second half of the talk it is discussed how the phase field approach can be used to couple the evolution of the dislocation system to the evolution
 of other field like solute atom concentration.