Memory, irreversibility and a non-equilibrium phase transition in cyclically sheared amorphous solids

Experiments and simulations of amorphous solids plastically deformed by a slow oscillatory drive at low temperatures, have uncovered a surprising 

phenomenon: for small strain amplitudes, the dynamics can be reversible, contrary to the usual notion of plasticity as an irreversible form of deformation. 

This reversibility allows the system to reach, after several training cycles, limit cycles in which plastic events repeat indefinitely under the oscillatory drive, demonstrating a form of material memory. However, as the strain amplitude is increased, the number of training cycles needed to reach a limit cycle diverges, preventing the system from reaching periodic states. This divergence, considered a phase transition, is dubbed "the reversibility-irreversibility transition". The nature and origin of this transition and its relation to irreversibility transitions in other systems remain subjects of debate. 

We will show that a graph representation of the dynamics, and the use of simple toy models of hysteresis, allows us to explore and explain some of the features observed in experiments and simulations.