  The magnetic flux dynamics of type-II superconductors within the critical
state regime is posed in a generalized framework, by using a variational theory
supported by well established physical principles. The equivalence between the
variational statement and more conventional treatments, based on the solution
of the differential Maxwell equations together with appropriate conductivity
laws is shown. Advantages of the variational method are emphasized, focusing on
its numerical performance, that allows to explore new physical scenarios. In
particular, we present the extension of the so-called double critical state
model to three dimensional configurations in which only flux transport
(T-states), cutting (C-states) or both mechanisms (CT-states) occur. The theory
is applied to several problems. First, we show the features of the transition
from T to CT states. Second, we give a generalized expression for the flux
cutting threshold in 3-D and show its relevance in the slab geometry. In
addition, several models that allow to treat flux depinning and cutting
mechanisms are compared. Finally, the longitudinal transport problem (current
is applied parallel to the external magnetic field) is analyzed both under T
and CT conditions. The complex interaction between shielding and transport is
solved.
