How to extract memories from a relaxing granular material

Recent experiments on crumpled sheets have found they can store multiple memories of past loading, and that one can simply watch the system relax over long timescales to read off its memories [1]. The model used to explain the observed nonmonotonic relaxation approximates the system as a population of exponentially relaxing modes with a specific distribution of timescales, though the physical manifestation of the modes in these systems remains ambiguous.
Here we show a granular packing can also exhibit history-dependent and nonmonotonic stress relaxation. We then expand upon the framework to understand glassy dynamics in disordered systems with the following results and insights. First, the history dependence of the relaxation is found to be tied to the shear stresses supported by the granular packing but not isotropic compressive stresses. Second, we extend the above model to incorporate finite duration loading. Third, with frictional contacts in the granular packing as the relaxing elements, each sliding glacially slowly, we move beyond relaxation experiments to explain features in the data of shape-dependent plasticity [2] as well as volumetric compaction and hysteresis during cyclic loading.
[1] Lahini et al., PRL 118, 085501 (2017).
[2] Murphy et al., arXiv:1808.06271v2 (2018).