Multiperiodic orbits from interacting soft spots in cyclically-sheared amorphous solids

TL;DR

This paper investigates how interacting soft spots in cyclically-sheared amorphous solids can lead to multiperiodic particle trajectories, revealing the role of frustration in these complex behaviors through a simple theoretical model.

Contribution

It introduces a minimal model of interacting soft spots that explains the emergence of multiperiodic orbits in amorphous solids under cyclic shear, highlighting the importance of frustration.

Findings

Multiperiodic orbits arise from interactions among three or more soft spots.

Frustrated interactions are essential for multiperiodic behavior.

The model suggests experimental signatures of frustration in amorphous solids.

Abstract

When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots -- locations where particles rearrange under stress and that resemble two-level systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.