Fig. 1
From: Bifurcation-based embodied logic and autonomous actuation
Overview of bifurcation-based actuation. a Schematic and photo of beams, with key geometric parameters and boundary conditions. b The normalized strain energy, E/(C10wLd), where C10 is a material parameter in the Holzapfel–Gasser–Ogden (HGO) model65 and d is the out-of-plane thickness of the beam; plots are included for a bistable beam (red curve, I) and a monostable beam (black curve, III) as a function of normalized displacement, u/Lsinθ, obtained via finite element simulations (Supplementary Note 5). Inset: photos of the undeformed (u = 0) and buckled configurations, corresponding to the two stable points (energy minima) on the bistable curve; the monostable curve has only the single minimum at u = 0. c Geometric phase diagram mapping geometric parameters to mechanical behavior, with schematic overlay indicating the transition from bistable to monostable (point I to point III) due to anisotropic swelling of the beams. Also shown are representative images recorded with a high-speed camera during actuation showing a unit when it is bistable (red), at the point of bifurcation when actuation occurs (green), and monostable (black). d A logic module which can act as one of several types of logic gates depending on the contents of the module. An AND gate can be constructed by using a hydrogel valve and a PDMS-GF15 bistable unit (requiring both water and toluene to switch from 0 to 1). An OR gate can be constructed by fabricating a composite bistable unit from both PDMS-GF5 (blue) and hydrogel (transparent) materials (this actuates if either water or toluene is applied); a functionally-complete NAND gate can be constructed by connecting two “input” bistable units to one “output” unit. In this case, only when toluene is applied to both input units will the output unit close from 1 to 0 (i.e., 1+1→0)
