Micromechanical aspects of granular ratcheting

The existence of granular ratcheting as a long-time behavior in granular materials is still under discussion in the scientific and engineering community. This behavior refers to the constant accumulation of permanent deformation per cycle, when the granular sample is subjected to loading-unloading stress cycles with amplitudes well bellow the yield limit. Ratcheting regimes are observed in both numerical and physical experiments. There is no controversy about the existence of ratcheting when the stress amplitudes reach the yield criterion. However, it is not clear whether this effect persists for loading amplitudes well bellow the yield limit, or whether there is a certain regime where no accumulation of deformation occurs. Early numerical simulations suggested that ratcheting may persist for extremely small loading amplitudes (Alonso-Marroquin and H. J. Herrmann, Rev. Lett. 92 5 (2004) 054301). More recent investigations drive to the conclusion that ratcheting at low stress amplitudes may be strongly influenced by the selection of the contact force (McNamara et al. Phys. Rev. E 77 (3) (2008) 31304). Here we present a numerical investigation of the dependence of granular ratcheting on contact force in a packing of spheres using the Cundall-Strack model and the McNamara correction to the contact force. We conclude that ratcheting for spherical particles is strongly influenced by the McNamara correction. The question of the existence of genuine ratcheting for small cycles for non-spherical particles is still unsolved.