Contact-mediated asymmetric delay and rate memory in snapping beam pairs

Abstract

Slender structures in dense environments interact through contact, which alters how and when they become unstable. Here we show that contact makes snap-through history dependent, so that when and whether a beam pair snaps depends on how long the contact is loaded. Under cyclic compression, the pair snaps on loading, snaps on unloading, or stays packed, with the loading and unloading rates selecting among the three. Upon contact, one beam rolls along the other without slip, and faster driving lets it roll further before it slides and snaps: to larger compression on loading and to smaller compression on unloading. This delay is asymmetric between loading and unloading as the unloading branch carries a memory of the loading rate. Interestingly, above a threshold compression the pair snaps even when the compression is stopped, with the time to snap diverging at that threshold. By exploiting this asymmetric, rate-dependent delay, we program ordered sequences of snap events in arrays of pairs with tunable gaps, and demonstrate that the energy dissipated per cycle becomes a two-parameter function of the loading and unloading rates, increasing fourfold when, at the fastest loading, the return is slowed.