Microscopic Models and Metamaterials with Memory

Models of interacting binary elements - hysterons - are simplified descriptions of the memory effects exhibited by driven, multistable systems - from crumpled sheets to frustrated metamaterials. After praising their effectiveness, we will discuss some of their shortcomings:

1) Even when driven quasistatically, the internal dynamics of physical systems containing hysterons can lead to transitions that are set dynamically. We create dynamically heterogeneous metamaterials and show how damping can promote avalanches, select transitions, and selects pairs of transitions that are inconsistent with any quasistatic hysteron model.

2) Two-dimensional networks of physical hysterons allow to probe how geometry controls the hysteron parameters. We show in particular how the angle between connected hysterons controls their interaction coefficients. Surprisingly, even a trigonal hub containing three physical hysterons exhibits transitions inconsistent with any quasistatic hysteron model.

3) Ensembles of randomly coupled hysterons lead to ill-defined responses (self-loops), with a probability that asymptotes to one for large ensembles. We introduce several restricted ensembles of interacting hysterons that are well behaved, allowing to study their statistics, and pose the general question which ensembles are well-defined.