Complex pathways and memory in compressed corrugated sheets

Abstract

The nonlinear response of driven complex materials—disordered magnets, amorphous media, and crumpled sheets—features intricate transition pathways where the system repeatedly hops between metastable states. Such pathways encode memory effects and may allow information processing, yet tools are lacking to experimentally observe and control these pathways, and their full breadth has not been explored. Here we introduce compression of corrugated elastic sheets to precisely observe and manipulate their full, multistep pathways, which are reproducible, robust, and controlled by geometry. We show how manipulation of the boundaries allows us to elicit multiple targeted pathways from a single sample. In all cases, each state in the pathway can be encoded by the binary state of material bits called hysterons, and the strength of their interactions plays a crucial role. In particular, as function of increasing interaction strength, we observe Preisach pathways, expected in systems of independently switching hysterons; scrambled pathways that evidence hitherto unexplored interactions between these material bits; and accumulator pathways which leverage these interactions to perform an elementary computation. Our work opens a route to probe, manipulate, and understand complex pathways, impacting future applications in soft robotics and information processing in materials.

Sequential Snapping and Pathways in a Mechanical Metamaterial

“…As the defect beams are strongly pre-curved, they do not exhibit buckling. We label the unsnapped and snapped states of the defect beam as 's = 0' and 's = 1', to stress that the defect beam acts as a mechanical hysteron 5,11 .…”

“…Hysteretic elements commonly occur in complex materials and play a key role in the understanding of memory effects [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] . Intuitively, when cyclically driving a complex system, one imagines these elements to undergo sequences of flipping transitions associated with hopping between metastable states.…”

“…. }, and represent these in a transition graph (t-graph) which takes the form of a directed (multi)graph 1,2,[6][7][8]11,18 . The (topological) organization of such t-graphs characterize the complex response of complex media and in particular memory effects such as Return Point Memory (RPM), transient memories, and subharmonic response 1,2,[4][5][6][7][8]12,[18][19][20] .…”

“…Controlling, characterizing and manipulating such hysterons is challenging in disordered systems such as crumpled sheets and amorphous media 10,11,[21][22][23][24][25] . Here we propose instead to leverage the design freedom of mechanical metamaterials to embed hysterons into a flexible metamaterial [13][14][15][16][17]26,27 .…”

“…We show that tuning their design parameters allows to access qualitatively different pathways. Moreover, we use gradients in the boundary conditions to independently tune the effective switching fields of the hysterons, thus obtaining multiple pathways from a single sample 11 . Finally, we show how subtle frictional effects allow to slowly evolve the switching fields, giving rise to a history dependent response beyond that captured by simple hysteron models.…”