The delicate memory structure of origami switches

Abstract

While memory effects emerge from systems of wildly varying length-and time-scales, the reduction of a complex system with many interacting elements into one simple enough to be understood without also losing the complex behavior continues to be a challenge. Here, we investigate how bistable cylindrical origamis provide such a reduction via tunably-interactive memory behaviors. We base our investigation on folded sheets of Kresling patterns that function as two-state memory units. By linking several units, each with a selected activation energy, we construct a one-dimensional material that exhibits return-point memory. After a comprehensive experimental analysis of the relation between the geometry of the pattern and the mechanical response for a single bit, we study the memory of a bellows composed of 4 bits arranged in series. When these bits are decoupled, the system reduces to the Preisach model and we can drive the bellows to any of its 16 allowable states by following a prescribed sequence of compression and extension. Moreover, we show how to reasonably discriminate between states by measuring the system's total height and stiffness near equilibrium. In bellows with coupled bits, the interactions alter the energy landscape and enable geometrically-disallowed defective stable configurations; this produces a 64-state configuration space with a more complex transition pattern. Using empirical considerations of the mechanics, we analyze the hierarchical structure of the corresponding diagram, which includes Garden of Eden states and subgraphs. We highlight two irreversible transformations, shifting and erasure of the defect, leading to memory behaviors reminiscent of those observed with more complex glassy systems.

Non-orientable order and non-Abelian response in frustrated metamaterials

“…We now show that the topologically protected zerodeformation nodes and lines realise the elementary units of robust mechanical memory based on non-Abelian response. Storing, reading and erasing mechanical informa-tion require the deformations to depend on the history of the loading sequence [5][6][7][8][9][10][11][12]. One strategy consists in applying multiple loads to a material having a non-Abelian response, deformations that depends on the sequential order of the loads.…”

“…Our metamaterials escape the traditional classification of order by symmetry breaking. Considering more general stress distributions, we leverage non-orientable order to engineer robust mechanical memory [5][6][7][8][9][10][11] and achieve non-Abelian mechanical responses that carry an imprint of the braiding of local loads [12,13]. We envision this principle to open the way to designer materials that can robustly process information across multiple areas of physics, from mechanics to photonics and magnetism.…”

Profusion of Transition Pathways for Interacting Hysterons

“…These can be modeled as hysterons, two-state elements which switch between phases "0" and "1" when the global driving field U passes through the upper and lower "bare" switching fields u + i or u − i (Fig. 1) [13,[15][16][17][18][19][20][21][24][25][26][27]. Indeed, collections of non-interacting hysterons-the well-studied Preisach model-describe surprisingly complex sequences of transitions and satisfy RMP [13,16,17,20,21,27].…”

“…1) [13,[15][16][17][18][19][20][21][24][25][26][27]. Indeed, collections of non-interacting hysterons-the well-studied Preisach model-describe surprisingly complex sequences of transitions and satisfy RMP [13,16,17,20,21,27].…”

“…Interactions are to be expected [13,17,22,25,26] and while non-interacting hysterons switch their phases indepedendent of each other, in sequences determined by the order of their bare switching fields, interactions scramble and entangle these switching orders. To characterize the response of coupled hysterons we use transition graphs (t-graphs), a recently introduced representation that captures all pathways of a complex system and aids in probing memory effects [13,[20][21][22][23][24][25][26][27]. We show that interactions mushroom the number of t-graphs, which feature transitions (avalanches, pseudo-avalanches, multi-edges) and topological structures (subharmonic cycles, breakdown of RPM) completely distinct from the Preisach model.…”