The origin of multi-periodic cycles in cyclically sheared amorphous solids

Plasticity in amorphous materials, such as glasses, colloids, or granular materials, is mediated by immobile local rearrangements called "soft spots" or "shear transformation zones." Experiments and simulations have shown that soft spots are two-state entities interacting via quadrupole displacement fields generated when they switch states. When a system is subjected to cyclic strain driving, soft spots can return to their original state when the strain direction reverses. In this case, the system may cycle periodically between the same microscopic states, with a periodicity that is a multiple of the period of the external drive. In this work, we focus on cycles that have periodicity larger than the periodicity of the drive. We use particle simulations to create graphs representing the system's different states. We use the graph topology and comparison between the displacement fields generated by the soft spots to identify all the soft spots active during such a cycle. We combine these results with a model of interacting hysterons (an abstraction of two-level systems) and show that multi-periodicity results from periodic stability oscillations of some soft spots around the drive amplitude. We then discuss the conditions and mechanisms which allow these oscillations to occur.