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An important aspect of the physics of amorphous solids is the onset ofirreversible behavior usually associated with yield. Here we study amorphoussolids under periodic shear using quasi-static molecular dynamics simulationsand observe a transition from reversible to irreversible deformation at acritical strain amplitude. We find that for small strain amplitudes the systemexhibits a noisy but repetitive limit-cycle, similar to return point memory\cite{sethna1993hysteresis}. However, for large strain amplitudes the behaviorbecomes chaotic (shows sensitivity to initial conditions) and thusirreversible. We show that the chaotic behavior is a result of the shear bandinstabilities that arise for large strains and the convective displacementfields they create.

Onset of Irreversibility and Chaos in Amorphous Solids Under Periodic Shear