Strength of Mechanical Memories is Maximal at the Yield Point of a Soft Glass

We show experimentally that both single and multiple mechanical memories can be encoded in an amorphous bubble raft, a prototypical soft glass, subject to an oscillatory strain. In line with recent numerical results, we find that multiple memories can be formed sans external noise. By systematically investigating memory formation for a range of training strain amplitudes spanning yield, we find clear signatures of memory even beyond yielding. Most strikingly, the extent to which the system recollects memory is largest for training amplitudes near the yield strain and is a direct consequence of the spatial extent over which the system reorganizes during the encoding process. Our study further suggests that the evolution of force networks on training plays a decisive role in memory formation in jammed packings.

Figure 1

(a) Snapshot of bubble raft. Ratio of number of small bubbles $N_S$ to large bubbles $N_L$ is $N_S/N_L\approx 1.9$. (b) Amplitude sweep measurements to quantify the yield point ${\gamma }_y$. Elastic and viscous moduli, $G^{\prime }$ (black circles) and $G^{\prime \prime }$ (red squares), respectively, versus amplitude of cyclic shear, ${\gamma }_{\circ }$. Vertical line is drawn at ${\gamma }_y=0.06$. The variances in particle positions attained at steady state on writing memory, ${⟨{\delta r}^2⟩}_{\infty }$ (Supplemental Material, Fig. S2 [24]), are shown as blue diamonds. (c) Typical write and read protocol followed in our experiments. Data correspond to training at strain amplitude of ${\gamma }_t=0.056$. Writing is done for $n=17$ cycles. Memory was read (blue-shaded region) after a 10 s pause after writing (white-shaded region). (d) Evolution of the variance in particle positions $⟨{\delta r}^2⟩$ during read for the untrained system (black squares) and for training at ${\gamma }_t=0.056$ (red circles). The horizontal dashed line represents the average noise floor in our experiments (Supplemental Material, Sec. C). (e) Multiple memories: The fraction of active particles, $f_{\mathrm{ac}}$ (i.e., fraction of particles with $⟨{\delta r}^2⟩>0.1\sigma$), versus ${\gamma }_{\circ }$ during read, showing two drops at ${\gamma }_{\circ }\approx 0.042$ and ${\gamma }_{\circ }\approx 0.053$. Multiple memories were more evident in $f_{\mathrm{ac}}$ (in the Supplemental Material, Fig. S6 shows signatures of multiple memories in $⟨{\delta r}^2⟩$ [24]).

Figure 2

(a) Representative read profiles for ${\gamma }_t$s across ${\gamma }_y$. (b) Strength of memory, $\mathrm{\Delta }$ [Fig. 1, defined as the ratio of $⟨{\delta r}^2⟩$ of the untrained to the trained raft at ${\gamma }_{\circ }={\gamma }_t$], versus ${\gamma }_t$ (filled red circles). Width of the active region $\delta b$ shown by hollow blue circles. Preyield regime is shaded gray. (c)–(e) Stroboscopic images of the raft during read, corresponding to points labeled 1 (onset of drop in $⟨{\delta r}^2⟩$), 2 (minimum in $⟨{\delta r}^2⟩$), and 3 (onset of second plateau in $⟨{\delta r}^2⟩$) in Fig. 1, respectively. Particles are color coded according to the magnitudes of their displacements.

Figure 3

(a) Strain rate $\dot{\gamma }$ as a function of $r/R_i$ for ${\gamma }_t=0.028$ (black squares), ${\gamma }_t={\gamma }_y=0.060$ (wine-red diamonds), and ${\gamma }_t=0.071$ (violet right triangles). $r$ is the distance from the center of the inner moving plate, and $R_i$ is the radius of the inner rotating disk. (b) and (c) $f_{\mathrm{ac}}$ as a function of $r/R_i$ for the 2nd and the 16th training cycles, respectively. ${\gamma }_t=0.028$ (black squares), ${\gamma }_t=0.049$ (red hollow circles), ${\gamma }_t={\gamma }_y=0.060$ (wine-red open diamonds), ${\gamma }_t=0.071$ (violet right triangles), and ${\gamma }_t=0.105$ (pale-green pentagons). (d) $\delta A$ versus ${\gamma }_t$.

Figure 4

(a) Schematic of force chains in jammed packings immediately after strain reversal. Although the particle configuration remains identical after reversal, the contact network is not. (b) Particle displacement map for ${\gamma }_{\circ }=0.073$ during read. This strain corresponds to the maximum before the drop (equivalent of point labeled 1) for a ${\gamma }_t=0.079$. (c) Particle displacement map after the first cycle of write for ${\gamma }_t=0.071$, which is closest to point 1 in our study.