Hysterons and Pathways in Mechanical Metamaterials

Mechanical metamaterials are carefully engineered materials whose proper-
ties are controlled by their structure, not by their composition, which allows
using metamaterials to study and control physical effects in detail. Here we
develop metamaterials to study the sequential, complex response of frustrated
materials that are cyclically driven. In particular, we focus on metamaterials
that act as collections of hysteretic, bistable elements called hysterons. We
create hysterons in metamaterials by using local frustration at defects and by
using a competition between two global, incompatible deformations modes. We
show how we can tune these hysterons, both by rational design and by using
spatial gradients in the mechanical driving. Then we show that collectively, our
samples exhibit complex transition pathways, including those with avalanches,
and study the role of hysteron interactions. Finally, we explore how to control
the frustration by local defects in so-called monoholar metamaterials.