Onset of Irreversibility and Chaos in Amorphous Solids Under Periodic Shear

TL;DR

This paper investigates the transition from reversible to irreversible behavior in amorphous solids under periodic shear, revealing a critical strain amplitude where chaos and shear band instabilities emerge, using molecular dynamics simulations.

Contribution

It demonstrates the onset of chaos and irreversibility in amorphous solids under periodic shear, linking shear band instabilities to chaotic dynamics.

Findings

Reversible limit-cycle behavior at small strains

Chaotic and irreversible behavior at large strains

Shear band instabilities cause chaos

Abstract

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