Figure 3. Curling mechanisms of inner and outer stems.

(a) The curling patterns of virtual stems with power-law hydro-actuation strain gradient (κ = a^r+1s^r) for different r exponents when η = 24. The dotted line shows the initial undeformed state. The deformed shape of the dehydrated (b) outer and (c) inner stems of S. lepidophylla are reproduced using large deformation FE simulations by setting η = κ* and are overlaid (solid lines) on stem images. The curvature of the non-inner stem model is constant (κ* = 3.93), whereas for the inner stem model, the curvature varies linearly with the stem length (κ* = 1.6 + 13.64 s*). (d) A simplified FE model for hydro-responsive curling of S. lepidophylla plants showing the cooperative packing of outer and inner stems at different stages of dehydration. The contours represent the absolute rotation of the stems in radian. Note that in actual S. lepidophylla plants, the spiral phyllotaxy would yield a gradient of curvature moving from the centre of the plant. Also, both the properties of the inner stems, and their shading by the more rapidly closing outer stems would slow their dehydration process, thus the timing of the movement of the inner stems would be delayed in real plants.