Fig. 2: Numerical and experimental investigations of the folding principle.

a Electrothermal stimulation exhibits spatially localized response of temperature T. Scale bars, 15 mm. b Whole-body FEA prediction on the dual, apposite vertical folding configuration. The multi-physical computation displays spatially localized response of temperature T, von Mises stress σ, and maximum principal strain ε, with respect to inlet energy q. Scale bars, 15 mm. c Contours traced along the edge when folded in response to temperature variations represented by its center value. The inset shows a photograph of the applied folding configuration (stimulated region depicted in red), along with graphical illustration of the associated coordinate system (x-, z-axis). d The curvature (κ) distribution of the contours shown in (c). The inset shows the graphical illustration for defining curvature κ. The gray box represents the region of activation. e Spatial consistency of folding response in various folding configurations. Each line represents the region of folding, with the color indicating the value of κavg, curvature averaged along the deformed curve, resulting from the consistent inlet energy density stimulation. f Folding response to 1000 cycles (n) of toggled stimulation inducing a folding configuration identical to (c, d).