Multiperiodic orbits in a model of interacting soft spots in cyclically-sheared amorphous solids*

When an amorphous or disordered solid is sheared repeatedly, it may reach a steady state in which the constituent particles travel in closed loops in space that repeat in every cycle. Recently an even more remarkable variant has been noticed in simulations, where the period of particle motions is a multiple of the period of driving. The reasons or conditions for this behavior have remained unclear. We investigate multiperiodicity in a simplified coarse-grained model of soft spots—locations where particles rearrange under stress—and we identify simple routes to multiperiodic behavior. We show how strong interactions and frustration could cause this behavior to emerge locally within a much larger system. Such conditions would also correspond to the breakdown of the return-point memory behavior that has been seen in these systems. Our work suggests promising directions for seeking multiperiodic behavior in experiments.