Correlated crackling and avalanches during slow relaxation of crumpled sheets

Crumpling a thin sheet of elastic material such as Mylar into a three dimensional structure results in the formation of a soft metamaterial with unusual, glass-like mechanical properties such as logarithmic relaxation or Kovacs-like memory effect.
As the crumpled ball relaxes or evolves, it emits crackling sounds, a result of multiple, localized micro-mechanical relaxation events within the sheet. These events are temporally correlated and occasionally group into avalanches, showing that the localized micro-relaxations are coupled. Moreover, the instantaneous crackling rate and macroscopic relaxation rate are proportional throughout the dynamics, all hinting at a connection between the coupled localized dynamics and the glassy-like macroscopic behavior.
To address this hypothesis, we present a statistical analysis of the correlated crackling and avalanches in four different experimental protocols - logarithmic relaxation under load, Kovacs-like memory retention under load switching, cyclic strain training and unconstraint spontaneous expansion of the sheet. Our results shed light on the dynamics of the coupled micro-mechanical relaxation events in each case, and suggest a possible mechanical mechanism for the observed glass-like behaviors.