Characterization of the material response in granular ratcheting

The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading. In this state, the system accumulates a small permanent deformation after each cycle. The value of this permanent strain accumulation becomes independent of the number of cycles after a short transient regime. We show in this paper that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. The definition of these variables is such that they can be easily measured both in the experiments and in the simulations. A thorough investigation of the micro- and macromechanical factors affecting these variables has been carried out by means of molecular-dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with periodically varying 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. Especially illustrative is the influence of the peculiar hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.