Marginal stability in memory training of jammed solids

Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly sheared with cycles of the same strain amplitude, it optimizes its mechanical response to the cyclic driving and stores a memory of it. We study memory by cyclic shear training as a function of the underlying stability of the amorphous structure in marginally stable and highly stable packings, the latter produced by minimizing the potential energy using both positional and radial degrees of freedom. We find that jammed solids need to be marginally stable in order to store a memory by cyclic shear. In particular, highly stable packings store memories only after overcoming brittle yielding and the cyclic shear training takes place in the shear band, a region which we show to be marginally stable.

Figure 1

Stress vs strain curves for highly stable (blue) and marginally stable (green) packings produced at pressure $P_0\simeq 0.08$ and composed of $N=4096$ particles. The stress is scaled by its typical value ${\sigma }_{\infty }$ in the plastic regime after yielding. Inset: Yielding stress ${\sigma }_Y$ as a function of the initial pressure $P_0$ at which brittle packings are produced.

Figure 2

(a) Pressure change $\delta P$ required to push a packing to a nearby instability as a function of the applied strain $\gamma$ averaged over 20 samples for both highly stable (blue) and marginally stable (green) packings of $N=4096$ particles. The dotted line indicates the average yielding strain of highly stable packings. (b) Magnitudes of the first 20 low-frequency eigenvectors, averaged over slices of the system along the $x$ axis at zero strain (black), right after yielding at $\gamma =0.122$ (red), and in the plastic regime at $\gamma =0.3$ (yellow) for a highly stable packing. Data are shifted to center the shear band.

Figure 3

Readout shear: ${\mathrm{\Delta }}_{\text{cycle}}$ as a function of the strain amplitude $\gamma$ for (a) untrained and (b) trained configurations of highly stable (blue) and marginally stable (green) packings. The solid red line indicates the encoded strain amplitude, ${\gamma }_{\text{train}}=0.15$, and the dashed black line shows the average yielding strain for highly stable packings.

Figure 4

Number of training cycles required to encode a memory, $N_{\text{cycles}}$, as a function of the encoded strain amplitude ${\gamma }_{\text{train}}$ for brittle (blue) and ductile (green) packings as well as brittle packings that are broken with a single cycle of strain amplitude of ${\gamma }_{\text{break}}=0.2$ (pink), 1 (red) and 5 (yellow) before the training. Inset: Shear band size $\delta$ as a function of ${\gamma }_{\text{break}}$ after training a memory of ${\gamma }_{\text{train}}=0.15$ with the same color code as in the main plot. The error bars represent the standard error on the mean.