Nonmonotonic Aging and Memory Retention in Disordered Mechanical Systems

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.

Figure 1

Two disordered mechanical systems. (a) The network of creases decorating a crumpled sheet of Mylar. Inset: a crumpled Mylar ball. (b) Stress relaxation of the crumpled ball with $H_1=45\mathrm{mm}$, $\delta =H_1-H_2=5\mathrm{mm}$. The dashed line is a fit to a logarithmic decay. (c) Nonmonotonic relaxation of crumpled Mylar, initially compressed by $\delta =5\mathrm{mm}$ for $t_w$ and then released by $\mathrm{\Delta }=2\mathrm{mm}$. (d) Typical microscopic image of the cross section of a PVC foam. Inset: elastic foam samples. (e) Stress relaxation of elastic foam with $H_1=18\mathrm{mm}$ and $\delta =4\mathrm{mm}$. The dashed line is a fit to $F=a+b\log (t)+c\log (t+t_0)$. Inset: $t_0$ vs $\delta$. (f) Nonmonotonic relaxation for elastic foam with $\delta =3\mathrm{mm}$ and $\mathrm{\Delta }=1.5\mathrm{mm}$.

Figure 2

Reproducible stress relaxation. (a) Crumpled Mylar: The relaxation rate $b$ vs the normal force at $t=1\mathrm{s}$, $F(t=1\mathrm{s})=a$. The different symbols represent experiments performed with different values of $\delta$. The normal force for which $b=0$ is marked as $F1$ (dotted blue line). (b) Same as (a) for elastic foams, where here $F_N(t=1\mathrm{s})=a+c\log (t_0+1)$ and we fit each relaxation curve to $F_N(t)=a+b\log (t)+c\log (t+t_0)$.

Figure 3

Memory effect. Linear scaling between the peak time and the waiting time for different values of $\mathrm{\Delta }$, shown for (a) crumpled thin sheets and (b) elastic foams. Insets: peak time vs $H_1-H_3$ for $t_w=20\mathrm{s}$.

Figure 4

Phenomenological model. Simulation of Eq. (3) for $V_1^{\mathrm{eq}}=1$, $V_2^{\mathrm{eq}}=0.2$, $V_3^{\mathrm{eq}}=0.5$, and $t_w=30$. The instantaneous amplitude of the relaxation modes are shown for (a) $t=t_w$ and (b) $t=t_p$. The slow modes with $\lambda >1/t_w$ and the fast modes with $\lambda <1/t_w$ are depicted on the left and right, respectively. The width of the bars represents the abundance of the different relaxation times according to $P(\lambda )\propto 1/\lambda$. Insets: total amplitude as a function of time calculated by summing over all the individual modes.

Figure 5

Universal relaxation dynamics. (a) $t_p/t_w$ vs $(F_2-F_3)/(F_3-F_1)$ for all the experiments performed on crumpled sheets (blue circles) and elastic foams (red squares). (b) Single-parameter fits for the nonmonotonic relaxation of Mylar sheets to $A-B[(F_3-F_2)\log (t)+(F_2-F_1)\log (t+C{t}_w)]$ with $B=A\times 0.025$ and $C=2.55$.