Fig. 2.

Characterization of saddle-shaped laminae. (A) A saddle shaped lamina corresponding to a scaled width w = 10, growth exponent n = 10, scaled maximum growth strain βw ² = 6.5 and κ_x w ² = 1.9. (B) The postbuckling behavior shows the scaled curvature κ_x w ² vs. βw ² on a log-log plot; the results for different w collapse onto a single curve. The Inset shows that the onset of buckling occurs via a supercritical pitchfork bifurcation, with κ_x w ∼(β − β*)^1/2, with β*w ² ≃ 2.51 for all values of the growth exponent n; only the positive branch is meaningful here. (Notation: S-stable, U-unstable.) (C) Cross-sectional profile f(y) for different values of the maximum growth strain β, when the critical growth strain β*w ² = 2.51 and w = 100.