Global memory from local hysteresis in an amorphous solid

Abstract

A disordered material that cannot relax to equilibrium, such as an amorphous or glassy solid, responds to deformation in a way that depends on its past. In experiments we train a 2D athermal amorphous solid with oscillatory shear, and show that a suitable readout protocol reveals the shearing amplitude. When shearing alternates between two amplitudes, signatures of both values are retained only if the smaller one is applied last. We show that these behaviors arise because individual clusters of rearrangements are hysteretic and dissipative, and because different clusters respond differently to shear. These roles for hysteresis and disorder are reminiscent of the returnpoint memory seen in ferromagnets and many other systems. Accordingly, we show how a simple model of a ferromagnet can reproduce and key results of our experiments and of previous simulations. Unlike ferromagnets, amorphous solids' disorder is unquenched; they require "training" to develop this behavior.We are familiar with our own memory and forgetfulness, and digital memories are woven into our lives. But throughout our environment, matter is being driven without relaxing to equilibrium, potentially forming memories of its own: specific information about past conditions that can be recalled later. As a simple example, rubber "remembers" the extrema of all deformations since it was cured [1]; the material stiffens as it is driven beyond those limits, allowing the memory to be read. Further afield, dilute non-Brownian suspensions that are sheared cyclically [2, 3] and charge density-wave conductors given electrical pulses [4,5] share distinctive rules for remembering multiple input values. Studying memory can thus reveal unexpected connections between systems and prompt new examinations of their physics [6].Recently, a new memory behavior was discovered in amorphous solids [7]. This vast class of materials features atoms or particles packed with a minimum of the regular placement found in crystals. Amorphous solids made of molecules, bubbles, macroscopic grains, or colloidal particles ( Fig. 1a) deform in remarkably similar ways: applied stress tends to cause localized clusters of particles ("soft spots") to rearrange, marking transitions among a vast set of metastable states [8][9][10]. Yet under oscillatory shear, after many cycles these rearrangements can become periodic; particles' trajectories become loops [7,[11][12][13][14][15]. Molecular dynamics simulations of glasses [7,16,17] and experiments on bubble rafts [18] showed that after a strain amplitude γ 1 has been applied repeatedly to reach a "trained" steady state, the material retains an imprint of its training: a readout protocol can reveal γ 1 . This protocol is illustrated in Fig. 1b: cycles of increasing amplitude γ read are applied, beginning with an amplitude below the training value [2, 3, 18]. After each cycle, one measures the mean squared displacement (MSD) of the particles, relative to the trained state. A local minimum in the MSD as a function of γ read shows evidence of the t...

Minimal descriptions of cyclic memories

“…those establishing the existence of a state {2}*—is enough to demonstrate that the memory behaviour is distinct from RPM. Likewise, in experiments and simulations with amorphous solids, summarized in figure 9 b , we can identify an analog of each state in figure 7 a , show the absence of an absorbing state, and demonstrate that memory content depends on which amplitude was applied last, suggesting a behaviour similar to RPM [24,34].

Figure 9.States and transitions consistent with experimental data.

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“…( a ) MTM in experiments on dilute non-Brownian suspensions, following structure of figure 1 [23]. ( b ) Behaviour similar to return-point memory, in experiments and simulations with two-dimensional amorphous solids, following structure of figure 7 a [24,34]. The notation ‘1111 …’ and ‘2222 …’ represents evolution over many cycles of driving until a steady state is reached; ‘22 …’ represents multiple cycles that do not reach a steady state.…”

“…We note that developing a reliable readout is essential for these applications. An example of a readout protocol is to drive the system with a series of increasing amplitudes and monitor its response as a function of amplitude [13,23,34]. In this case, one must be careful to ensure that the readout process does not introduce or erase memories before they are observed.…”

“…This by itself rules out RPM. The same test in amorphous solids does change the state (to {1, 2}) [34].…”

Embedding orthogonal memories in a colloidal gel through oscillatory shear

“…Indeed, similar memory effects have been found in experiments and simulations of model amorphous systems [2,9,10], granular systems [11], and glasses [12][13][14][15]. The interactions between particles can vary and even the nature of the reversibility can vary for different systems [9,[16][17][18][19][20]. The core idea of particles rearranging and exploring possible states to find a reversible one still applies, regardless of the specifics of the system.…”