Abrupt out-of-plane edge folding of a circular thin plate: Implication for a mature Victoria regia leaf

Multi-functional topology optimization of Victoria cruziana veins

The growth and development of biological tissues and organs strongly depend on the requirements of their multiple functions. Plant veins yield efficient nutrient transport and withstand various external loads. Victoria cruziana, a tropical species of the Nymphaeaceae family of water lilies, has evolved a network of three-dimensional and rugged veins, which yields a superior load-bearing capacity. However, it remains elusive how biological and mechanical factors affect their unique vein layout. In this paper, we propose a multi-functional and large-scale topology optimization method to investigate the morphomechanics of Victoria cruziana veins, which optimizes both the structural stiffness and nutrient transport efficiency. Our results suggest that increasing the branching order of radial veins improves the efficiency of nutrient delivery, and the gradient variation of circumferential vein sizes significantly contributes to the stiffness of the leaf. In the present method, we also consider the optimization of the wall thickness and the maximum layout distance of circumferential veins. Furthermore, biomimetic leaves are fabricated by using the three-dimensional printing technique to verify our theoretical findings. This work not only gains insights into the morphomechanics of Victoria cruziana veins, but also helps the design of, for example, rib-reinforced shells, slabs and dome skeletons.

Gigantic floating leaves occupy a large surface area at an economical material cost

The giant Amazonian waterlily (genus Victoria) produces the largest floating leaves in the plant kingdom. The leaves' notable vasculature has inspired artists, engineers, and architects for centuries. Despite the aesthetic appeal and scale of this botanical enigma, little is known about the mechanics of these extraordinary leaves. For example, how do these leaves achieve gigantic proportions? We show that the geometric form of the leaf is structurally more efficient than those of other smaller species of waterlily. In particular, the spatially varying thickness and regular branching of the primary veins ensures the structural integrity necessary for extensive coverage of the water surface, enabling optimal light capture despite a relatively low leaf biomass. Leaf gigantism in waterlilies may have been driven by selection pressures favoring a large surface area at an economical material cost, for outcompeting other plants in fast-drying ephemeral pools.

Buckling morphology of an elastic ring confined in an annular channel

This paper studies the buckling morphology transition of an elastic ring confined in an annular channel. Under uniform axial strain, the ring would first form one inward blister and then transit to an "S" shape, but does not induce more blisters due to an energy barrier caused by the annular shape of the channel. In order to overcome the energy barrier, external perturbation is employed and a stable morphology with multiple blisters may be obtained. A theoretical framework is then established to calculate the bifurcation points of the shape transition, which agrees well with finite-element (FEM) simulation results. The diagrams of the stable buckling morphologies with respect to the geometrics of the elastic rings are presented, which may provide useful insights for practical applications, for example, the design of a peristaltic pump.