Onset of irreversibility and chaos in amorphous solids under periodic shear

A fundamental problem in the physics of amorphous materials is understanding the transition from reversible to irreversible plastic behavior and its connection to yield. Currently, continuum material modeling relies on phenomenological yield thresholds, however in many cases the transition from elastic to plastic behavior is gradual, which makes it difficult to identify an exact yield criterion. Here we show that under periodic shear, amorphous solids undergo a transition from repetitive, predictable behavior to chaotic, irregular behavior as a function of the strain amplitude. In both the periodic and chaotic regimes, localized particle rearrangements are observed. We associate the point of transition from repetitive to chaotic behavior with the yield strain and suggest that at least for oscillatory shear, yield in amorphous solids is a result of a "transition to chaos."