Session X06: Memory Formation in Matter: Encoding, Reading, and Design

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Multistability—the property of having multiple stable equilibrium configurations—has recently emerged as a powerful platform to design a wide range of smart structures, including shape-reconfigurable architectures, fully elastic and reusable energy-trapping metamaterials, soft swimming robots with preprogrammed directional propulsion, and deployable solar panels for aerospace applications. Here, we focus on a model system comprising a 1D array of rigid blocks connected by rigid levers and a linear spring and use a combination of experiments and analyses to study the effect of geometric parameters on the deformation sequences that emerge when the displacement of the top unit is controlled. We then exploit these sequences to design a simple machine with programmable behavior.   

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We show how to construct metamaterials that exhibit a sequence of actions under monotonic input. We embed a number of defect beams in a biholey metamaterial, such that global compression induces snapping of the defect beams. We observe that compression yields a precise, mechanical pathway of snapping and unsnapping actions of the defect beams, which act as hysterons. We investigate systems with one and multiple defect beams, focusing on design rules for the amount of hysteresis of each hysteron, as well as their coupling. Our work opens a new route to design complex pathways in metamaterials.   

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Memory effects in disordered matter – granular suspensions, spin-glasses or crumpled paper - can be described via pathways between distinct states visited by the system upon driving. However, we lack experimental strategies to probe, understand and control such pathways.
Here we introduce mechanical driving of corrugated elastic sheets to precisely observe and manipulate complex, multi-step pathways. In particular we use tilting of the boundaries to elicit a multitude of pathways from a single sample. Strikingly, these include “scrambled” pathways, which provide compelling evidence of the effect of interactions on pathways. This work provides a new avenue to study memory and pathways in complex matter.   

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Many bulk materials can retain memories of their past; rocks and glasses may remember a stress that was previously applied or a temperature at which they were aged. Here we study a thin cylindrical shell under cyclic loading. Whereas previous work focused on the mechanical response of an already-crumpled film [1], we begin with a pristine film and study its route to steady states under a variety of cyclic driving protocols—in effect, converting pristine or lightly-crumpled raw material into a reliable structural component with memory. We combine acoustic, force, and optical measurements to capture reversible and irreversible changes to the folds and ridges in the sheet. Under cyclic axial compression, we see behaviors that are nominally consistent with return-point memory, but with pronounced aging effects—a combination of memory behaviors that may be relevant to other complex condensed matter systems. We also study how these behaviors are modified by introducing torsion of the cylinder as a second driving parameter.

[1] Lahini et al., PRL 118 (2017)   

Live

Crumpling a thin sheet endows it with unusual mechanical properties, such as an intermittent mechanical response and slow relaxation under load. One of the most staggering properties of crumpled sheets is their ability to retain memories - e.g., a memory of the largest load they have been subjected to, or the durations of past mechanical perturbations.

We study the behavior of crumpled sheets under cyclic strain. The mechanical response, as measured by stress-strain curves, converges to limit cycles with repetitive discrete stress drops. These, we show, encode a memory of the strain history of the sheet, particularly of the largest applied strain. We investigate how this phenomenon is encoded in the crumpled structure, and find that the stress drops are the result of hysteretic switching of localized degrees of freedom distributed across the sheet. We show that the observed memories emerge from the elastic coupling between these spatially localized hysterons, and demonstrate in numerical simulations that a simple model of coupled bi-stable elements captures many of the observed effects. Our studies reveal a hierarchical structure of internal states with both reversible and irreversible pathways, which we utilize to devise ways for encoding, retrieving and erasing memories.   

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The elastic response of ordinary materials typically satisfies the principle of superposition, thus rendering the deformation output impervious to the order of actuation inputs. This severely constrains the design of multifunctional programmable metamaterials. Here, we introduce an elegant solution in the form of non-commuting mechanical metamaterials, which are sensitive to the magnitude as well as the order of inputs. We discuss the essential ingredients to design such a non-commuting metamaterial and demonstrate a scalable framework to study them. Our work establishes the groundwork for reprogrammable designer matter with memory.   

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In the field of "artificial spin ice," great progress has been achieved concerning the intentional manipulation of frustration incorporated within arrays of magnetic dipoles. We present a mechanical analogue of artificial spin ice built up from bistable square cells that act as simple mechanical hysterons. These unit cells deform spontaneously, so that the metamaterial contains competing local ground-state orientations, which are separated by domain walls. Tuning the stiffness of elements in the unit cell, we can control the characteristic curvature and propagation speed of these domain walls. Under textured driving from the boundaries, the system exhibits dynamic hysteresis. Moreover, when driving the system from its boundary we can also observe multiple distinct steady states. These hysteresis cycles are a novel feature of our mechanical spin-ice analogue.This mechanical metamaterial exhibits a novel memory of the topology of its initial condition, and can thus have potential application in the development of a mechanical memory storage.   

Live

When sheared cyclically and quasi-statically, athermal jammed packings learn to visit precisely the same configurations on subsequent cycles. This periodicity encodes a memory of the applied shear amplitude [1]. Aspects of this behavior have been understood via a distribution in the material of non-interacting individual two-state configurations (hysterons) [2]. While successful in explaining many of the observed phenomena, this model fails to account for fundamental aspects including (i) that the period, T, of the response can be greater than one cycle and (ii) that it can take many cycles, τ, before the system falls into a periodic orbit. By introducing interactions between hysterons, we can produce situations where T > 1 and τ > 1. Our interacting model also reveals a novel memory of simultaneous multiple shear amplitudes which is distinct from that found in multiple transient memories because it does not appear as a local signature in the system response. Global measurements of this memory provide a measure of the interaction strength.
[1] D Fiocco, G Foffi, S Sastry, PRL 112, 025702 (2014).
[2] NC Keim, J Hass, B Kroger, D Wieker, PR Research 2, 012004(R) (2020).   

Live

When an amorphous or disordered solid is sheared repeatedly, it may reach a steady state in which the constituent particles travel in closed loops in space that repeat in every cycle. Recently an even more remarkable variant has been noticed in simulations, where the period of particle motions is a multiple of the period of driving. The reasons or conditions for this behavior have remained unclear. We investigate multiperiodicity in a simplified coarse-grained model of soft spots—locations where particles rearrange under stress—and we identify simple routes to multiperiodic behavior. We show how strong interactions and frustration could cause this behavior to emerge locally within a much larger system. Such conditions would also correspond to the breakdown of the return-point memory behavior that has been seen in these systems. Our work suggests promising directions for seeking multiperiodic behavior in experiments.   

Live

<div style="direction: ltr;">Experiments and simulations had shown that disordered systems subject to cyclic driving reach, after a training phase of multiple cycles, a periodic state which was shown to encode memory. In this state the particle trajectories form closed loops in space which repeat themselves every integer number of periods, thus it can be represented as a limit cycle in the configuration space, or the energy landscape of the system. The high dimensionality of this space renders it impractical to directly simulate dynamics on models of such landscapes, even for simple cases such as Gaussian surfaces. Here we use a novel simulation algorithm, that uses a sampling technique to simulate deterministic forced dynamics on a Gaussian landscape. We show that similarly to amorphous solids, this model undergoes a transition between periodic and a-periodic dynamics at a critical forcing amplitude with similar features to the transition observed in amorphous solids. This indicates that understanding the dynamics on simple models of random energy landscapes can give us valuable insights into the physics of memory retention in amorphous solids and other random materials.</div>   

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We analyze the directed graph of plastic transitions obtained by shearing an initial quenched configuration. We decompose the graph into strongly connected components (SCCs) whose configurations are mutually reachable, meaning that each configuration in this component can be reached from any other configuration in the same component by a series of plastic events. We call these transitions ``reversible’' whereas transitions that connect different configurations belonging to different strongly connected components are then called ``irreversible’', since these configurations are not mutually-reachable, meaning that there is no return path. We find that the distinction between reverible and irreversible transitions also manifests itself in the microscopical properties of the underlying plastic events - irreversible transitions typically correspond to significantly larger energy drops associated with larger plastic events. We further show that the size distribution of strongly connected components follows power-law scaling and hence large SCCs are rare. Since the states of limit cycles must necessarily belong to the same SCC, this also means that large limit-cycles are rare which is consistent with previous observations.   

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Non-orientability is a topological property, which presents it is unable to make a consistent choice of surface normal vector at every point. Because of this non-trivial topological property, non-orientability can create novel and unusual mechanical behaviour. However, the complex geometry of non-orientable structures limits their applications in the real world. Here we show that it is possible to achieve non-orientable mechanics in an orientable metamaterial, rotating-square mechanism. This is achieved by a geometrical frustration, which generates a single movable domain wall in periodic structures during loading. The moving path of the domain wall can be controlled by the loading sequence, which leads to different mechanical responses. In other words, our metamaterial can break abelian rules and has a mechanical memory. Based on it, we build a mechanical sequential logic gate, which can achieve the same value table as with a Set-Reset latch, one of the most basic sequential logic gates in electronic fields. The geometrical frustration design opens up a new avenue for new design of topological metamaterials, non-orientable metamaterials, non-abelian metamaterials and sequential logic gates.   

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Collections of two-state hysteretic elements called hysterons form a popular model to describe the intricate pathways, hysteresis loops and memory effects exhibited by driven complex media. While most studies have focused on independent hysterons, here we show that hysteron interactions have a dramatic effect on the qualitative nature and variety of these pathways and memory effects. Anti-ferromagnetic couplings in particular have a striking impact: hysteresis loops are no longer nested, subharmonic responses can arise, the distinction of ’up’ and ’down’ transitions become blurred, and in some cases the transition graph can only be described as a multi-graph. This work opens up new routes to study pathways and memory in complex media.