  A theoretical framework is presented, which allows to explain many
experimental facts related to pinning and cross-flow effects between flux tubes
in type-II superconductors. It is shown that critical state principles, in the
manner introduced by C. P. Bean for parallel vortex lattices, may be used to
describe the observed behavior. We formulate a least action principle, giving
place to a variational interpretation of the critical state. The coarse-grained
electrodynamic response of the superconductor is solved by minimizing the
magnetic field changes, for a current density vector constrained to belong to
some bounded set (Delta). It is shown that the selection of Delta determines
the specific critical state model in use. Meaningful choices of Delta are
discussed in view of the related physical mechanisms.
