Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids

Abstract

Plasticity in amorphous materials, such as glasses, colloids, or granular materials, is mediated by local rearrangements called "soft spots". Experiments and simulations have shown that soft spots are two-state entities interacting via quadrupolar displacement fields generated when they switch states. When the system is subjected to cyclic strain driving, the soft spots can return to their original state after one or more forcing cycles. In this case, the system has periodic dynamics and will always repeat the same microscopic states. Here we focus on multi-periodic dynamics, i.e. dynamics that has periodicity larger than the periodicity of the drive, and use a graph-theoretical approach to analyze the dynamics obtained from numerical simulations. In this approach, mechanically stable configurations that transform purely elastically into each other over a range of applied strains, are represented by vertices, and plastic events leading from one stable configuration to the other, are represented by directed edges. An algorithm based on the graph topology and the displacement fields of the soft spots reveals that multi-periodic behavior results from the states of some soft spots repeating after more than one period and provides information regarding the mechanisms that allow for such dynamics. To better understand the physical mechanisms behind multi-periodicity, we use a model of interacting hysterons. Each hysteron is a simplified two-state element representing hysteretic soft-spot dynamics. We identify several mechanisms for multi-periodicity in this model, some involving direct interactions between multi-periodic hysterons and another resulting from cooperative dynamics involving several hysterons. These cooperative events are naturally more common when more hysterons are present, thus explaining why multi-periodicity is more prevalent at large drive amplitudes.