Novel memory formation in interacting hysterons

When sheared cyclically and quasi-statically, athermal jammed packings learn to visit precisely the same configurations on subsequent cycles. This periodicity encodes a memory of the applied shear amplitude [1]. Aspects of this behavior have been understood via a distribution in the material of non-interacting individual two-state configurations (hysterons) [2]. While successful in explaining many of the observed phenomena, this model fails to account for fundamental aspects including (i) that the period, T, of the response can be greater than one cycle and (ii) that it can take many cycles, τ, before the system falls into a periodic orbit. By introducing interactions between hysterons, we can produce situations where T > 1 and τ > 1. Our interacting model also reveals a novel memory of simultaneous multiple shear amplitudes which is distinct from that found in multiple transient memories because it does not appear as a local signature in the system response. Global measurements of this memory provide a measure of the interaction strength.
[1] D Fiocco, G Foffi, S Sastry, PRL 112, 025702 (2014).
[2] NC Keim, J Hass, B Kroger, D Wieker, PR Research 2, 012004(R) (2020).