Fig. 2

Designs to optimize the out-of-plane displacements of two representative 2D precursors during tensile buckling. a Illustration of a 2D precursor in an arc geometry. b Experimental and FEA results on the intermediate states (I, II, and III, as marked in c) of the 3D assembly. c Measured and calculated maximum out-of-plane displacements (\(U_{3,{\mathrm{max}}}/L_{{\mathrm{max}}}\)) of the buckled configuration versus the tensile strain applied to the substrate, for the precursor design with parameters (θ, W/L, t/W, W) = (240°, 0.05, 0.1, 500 µm). d Experimental and FEA results on the normalized maximum out-of-plane displacements (\(U_{3,{\mathrm{max}}}^{{\mathrm{peak}}}/L_{{\mathrm{max}}}\)) versus the arc angle θ, for three different ratios (W/L = 0.025, 0.033, 0.05) and fixed parameters (t/W, W) = (0.1, 500 µm). e Illustration of the 2D precursor in a coil geometry consisting of three half-circles of different radii (R₁, R₂ and R₃). f Experimental and FEA results on the intermediate states (I, II, and III, as marked in g) of the 3D assembly. g Measured and calculated maximum out-of-plane displacements (U_3,max) of the buckled configuration versus the tensile strain applied to the substrate, for the precursor design with parameters (R₁/R₂, R₃/R₂, W/R₂, t/W, W) = (0.8, 1.6, 0.05, 0.1, 500 µm). h Experimental and FEA results on the normalized maximum out-of-plane displacements (\(U_{3,{\mathrm{max}}}^{{\mathrm{peak}}}/L_{{\mathrm{max}}}\)) versus the radius ratio R₁/R₂, for three different ratios (R₃/R₂ = 1.2, 1.6, 2.0) and fixed parameters (W/R₂, t/W, W) = (0.05, 0.1, 500 µm). The colors in the FEA results correspond to the maximum principal strains. The red regions of 2D precursors denote the parts bonded onto the substrate. Scale bars, 5 mm