Constructing the transition graphs of interacting hysterons

In a variety of frustrated mechanical systems, including crumpled sheets, origami structures and sheared amorphous solids, unusual pathways have been observed in response to external driving. These include breaking of return-point memory, multiperiodic response to cyclical driving, and transient memory. It turns out that such responses are captured by a model of interacting hysteretic bits, known as hysterons. While the Preisach model of non-interacting hysterons is well understood, interactions lead to a combinatorial explosion of possible responses. We present a strategy to hierarchically construct all state transition graphs for interacting hysterons. This provides us with a framework for understanding the memory phenomena that have been seen in experiment, and opens up the way for rational design of mechanical pathways.