Snapping and Switching of Elastic Arches with Patterned Preferred Curvature

Abstract: An elastic arch is an archetypal bistable system. Here, we combine elastica theory and photo-mechanical experiments to elucidate the mechanics of an active arch with a spatio-temporally varying preferred curvature $\overline κ(s)$. Our shallow-arch theory completely describes any such system via the decomposition of its $\overline κ(s)$ into Euler-buckling modes. Intuitively, if $\overline κ(s)$ overlaps with the fundamental mode, it snaps the arch up/down. Conversely, non-overlapping $\overline κ(s)$ drives a second-order transition to a higher-order shape. Furthermore, the form of $\overline κ(s)$ enables control over the instability's character; we find the forms for snapping with maximum energy release and at the lowest stimulation (both binary patterns) and design forms for symmetric and asymmetric switching pathways. Analogous control can also be achieved in boundary-driven instabilities of passive arches by fabricating them with suitable $\overline κ(s)$. We thus anticipate our results will improve switchable/snapping elements in MEMS, robotics, and mechanical meta-materials.