Memory behavior of a randomly driven model glass

TL;DR

The paper addresses whether memory for mechanical history can persist in disordered solids under fluctuating loads. The authors run atomistic simulations of a 2D Kob–Andersen glass and train it with a random-walk driven shear up to a maximal amplitude $\gamma_T$, then read out the memory using forward/reverse and two-cycle readouts to detect the training amplitude via the mean-squared displacement. They show memory forms below the yield strain $\gamma_{yield}$ and is robust to whether the training was random or deterministic, while being highly directional and retrievable only in the trained plane, with a Bauschinger-like asymmetry in the post-training response. Above the yield, irreversible rearrangements erase the memory. The study reveals universal, robust memory in glasses under stochastic driving and highlights the anisotropic character of history encoding that could inform design of history-dependent materials.

Abstract

We investigate by atomistic simulations the memory behavior a model glass subjected to random driving protocols. The training consists of a random walk of forward and/or backward shearing sequences bounded by a maximal shear strain of absolute value γT . We show that such a stochastic training protocol is able to record the training amplitude. Different read-out protocols are also tested and are shown to be able to retrieve the training amplitude. We then emphasize the ten- sorial character of the memory encoded in the glass sample and then characterize the anisotropic mechanical behavior of the trained samples.

Figures (4)

• Figure 1: (A) Illustration of the random driving protocol as a random walk along the strain axis with fixed strain step size $\delta \epsilon$ (indicated by the dashed red lines) and reflecting boundaries at $\pm \gamma_T$ (horizontal black dashed lines). A random driving cycle consists out of a first passage from the initial state $A$ to one of the reflecting boundaries, which is followed by a first passage to the opposite boundary and a subsequent (first) return to zero strain. The training by random cycles involves applications of multiple cycles with the same sequence of boundary visits as the first cycle, leading to the "trained" glass $T$. Without lack of generality these cycles can be rectified such that the first boundary visited always establishes the direction of positive shear. (B) Read-outs from $T$ are performed by applying one or two cycles of (deterministic) cyclic shear with read-out amplitude $\gamma_R$ that either have the same sense of driving as the random driving (FWD), or are out of phase with respect to it (REV). The states reached at the end of the first and second read-out cycles are denoted by $R_1$ and $R_2$, respectively. (C) The result of a read-out obtained by applying to $T$ FWD read-out cycles with different strain read-out amplitudes $\gamma_R$ and measuring the mean square displacement (MSD) between the particle configurations of $T$ and $R_1$. Shown are the result for a system with $N = 2000$ particles, trained at $\gamma_T = 0.05$ for various numbers of training cycles as indicated in the figure. The FWD MSD read-out curve develops a kink at a read-out amplitude matching the training amplitude (vertical dashed lines). Already after $30$ training cycles, this kink has developed into a local minimum so that the MSD vanishes when training and read-out strains match. (D) Comparison of FWD memory signals from samples trained either under a deterministic and or random cyclic shear protocol for $N = 2000$ and training amplitudes $\gamma_T = 0.04$ and $0.05$. For each training amplitude shown, annealing by deterministic and random cycling leads to nearly indistinguishable MSD read-outs.
• Figure 2: (A) The results of the four read-out protocols FWD, REV, FWD-FWD and REV-REV, applied to a glass subject to random cycling over $50$ training cycles at amplitude $\gamma_T = 0.05$. The FWD read-out shows a local minimum where the read-out and training amplitude match, as indicated by the black dashed vertical line. In the REV read-outs, the MSD increases with increasing $\gamma_R$ exhibiting a change of growth rate around $\gamma_R \approx \gamma_T$. Note that in the absence of the knowledge of the positive sense of shearing cyclic shear applied to a sample will result either in a FWD or REV read-out, which are qualitatively different. Conversely, the FWD-FWD and REV-REV exhibit nearly indistinguishable read-out responses and hence are independent on the orientation of the shear plane. Moreover, for the training amplitude shown the 2-cycle read-out signal remains close to zero rising sharply only when $\gamma_R > \gamma_T$. (B). Read-outs of a sample trained under random cycling by simple shear, but where read-outs are performed by deterministic cycles of pure shear, corresponding to compression and elongation of the sample along the horizontal and vertical axis such that the area remains constant. All four read-out protocols exhibit very similar MSD curves and moreover show no memory of the amplitude of training under simple strain.
• Figure 3: Mechanical stress-strain response after training. (A) stress-strain curves obtained in the forward and reverse direction i) for the pristine glass, ii) after deterministic cyclic training at $\gamma_T=0.05$ and, iii) after random training at $\gamma_T=0.05$. After mechanical annealing the trained glasses are stiffer and harder than the pristine glass. (B) Mechanical response of the same samples after prior unloading to a stress free state. After symmetrization of the reverse response, the pristine glass shows perfect symmetry between forward and reverse loading while the trained glasses show a significant asymmetry: after training the samples have become harder in the reverse direction than in the forward direction. (C) Mechanical response in the pure shear $xx-yy$ direction. Again, the pristine glass shows perfect symmetry between forward and reverse loading. This symmetry is also recovered for the trained sample.
• Figure A1: Response of read-out protocols applied to a glass sample trained at $\gamma_T = 0.11$ ($> \gamma_{\text{yield}}\approx 0.09$) for two different random walk step sizes --- $\delta\epsilon = 0.01$ and $0.005$. We don't observe any memory formation at training amplitude beyond yielding.