  Continuum dislocation dynamics (CDD) aims at representing the evolution of
systems of curved and connected dislocation lines in terms of density-like
field variables. Here we discuss how the processes of dislocation
multiplication and annihilation can be described within such a framework. We
show that both processes are associated with changes in the volume density of
dislocation loops: dislocation annihilation needs to be envisaged in terms of
the merging of dislocation loops, while conversely dislocation multiplication
is associated with the generation of new loops. Both findings point towards the
importance of including the volume density of loops (or 'curvature density') as
an additional field variable into continuum models of dislocation density
evolution. We explicitly show how this density is affected by loop mergers and
loop generation. The equations which result for the lowest order CDD theory
allow us, after spatial averaging and under the assumption of unidirectional
deformation, to recover the classical theory of Kocks and Mecking for the early
stages of work hardening.
