A Crumpled Sheet’s Remembrance of Things Past

Abstract

We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior. DOI: 10.1103/PhysRevLett.118.085501 Many disordered systems exhibit phenomenologically similar slow relaxation dynamics that may span many time scales-from fractions of a second to days and even years. Examples range from time-dependent resistivity in disordered conductors [1][2][3][4][5], flux creep in superconductors [6,7], dynamics of spin glasses [8][9][10][11], structural relaxation of colloidal glasses [12,13], time dependence of the static coefficient of friction [14][15][16], thermal expansion of polymers [17,18], compaction in agitated granular systems [19], and crumpling of thin sheets under load [20,21]. The ubiquity of slow relaxation phenomena suggests the existence of common underlying physical principles [9,[22][23][24][25][26][27]. However, as slow relaxation is usually a smooth, featureless process, it is hard to discern between the different descriptions using experiments. One way of probing deeper into the time-dependent properties of glassy systems is using a phenomenon known as aging, where the manner in which the system relaxes towards equilibrium depends on its history.In this Letter, we report nonmonotonic aging dynamics that give rise to a maximum in the relaxation curve. This extremum provides an unambiguous signature of aging and memory, as well as a clear, measurable time scale. We experimentally study two distinct disordered mechanical systems: crumpled thin sheets and elastic foams, shown in Fig. 1. When compressed, both systems exhibit monotonic, slow stress relaxation [Figs. 1(b) and 1(e)]. When the compression is decreased after a certain waiting time, the stress evolution remarkably becomes nonmonotonic: under constant compression, the measured normal force first increases slowly over seconds to hours, reaches a welldefined peak, and then reverses to a renewed slow relaxation [Figs. 1(c) and 1(f)]. In both systems, the stress peak time is linear in the waiting time, indicating that the different systems carry a similar, long-lasting memory of previous mechanical states. These observations are inconsistent with the single-parameter model used to explain logarith...

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