  The existence of a very special ratcheting regime has recently been reported
in a granular packing subjected to cyclic loading \cite{alonso04}. In this
state, the system accumulates a small permanent deformation after each cycle.
After a short transient regime, the value of this permanent strain accumulation
becomes independent on the number of cycles. We show that a characterization of
the material response in this peculiar state is possible in terms of three
simple macroscopic variables. They are defined that, they can be easily
measured both in the experiments and in the simulations. We have carried out a
thorough investigation of the micro- and macro-mechanical factors affecting
these variables, by means of Molecular Dynamics simulations of a polydisperse
disk packing, as a simple model system for granular material. Biaxial test
boundary conditions with a periodically cycling load were implemented. The
effect on the plastic response of the confining pressure, the deviatoric stress
and the number of cycles has been investigated. The stiffness of the contacts
and friction has been shown to play an important role in the overall response
of the system. Specially elucidating is the influence of the particular
hysteretical behavior in the stress-strain space on the accumulation of
permanent strain and the energy dissipation.
