Profusion of transition pathways for interacting hysterons

Abstract

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

Sequential Snapping and Pathways in a Mechanical Metamaterial

“…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.…”

“…To understand these sequences, it is often possible to model these elements as hysterons: hysteretic elements which which flip their internal state s from '0' to '1' when the local driving exceeds the upper switching field ε + , and which flip from '1' to '0' when the driving falls below the lower switching field ε − (Fig. 1a) 2,3,[6][7][8][9] . By specifying the values of the switching fields of a collection of hysterons, and potentially their interactions, one can determine the transitions between all collective states S := {s 1 , s 2 , .…”

“…. }, 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] .…”

Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids

“…We thus obtain only a limited amount of information about the pair-wise interaction between active soft spots present. To remedy this, we turn next to a model of interacting hysteresis elements, the interacting Preisach model, which was originally introduced by Hovorka and Friedman [20], and subsequently revisited within the context of memory formation in driven mechanical systems [7][8][9][10].…”

“…This mechanism involves two steps: the first step is a cascade of strain threshold shifts that causes some hysterons to switch prematurely, which then causes the γ + (γ − ) of one hysteron to go above (below) the strain amplitude. The second step is a scrambling [9,10] of the switching order of the hysterons involved in the cascade between the different forcing cycles. The periodic scrambling then causes the strain threshold of this hysteron to oscillate around the forcing amplitude, making the switching pattern of the hysteron multi-periodic.…”