Biomimetic Research for Folding and Unfolding Manners of Leaves and Flowers on Plants

本课题的研究内容之一就是揭示规则波纹单叶的展开方式，并注意到角梁展开时与普通杉木展开时叶片形状的不同，即角梁呈相对平坦的形状，而普通杉叶呈V形。通过对枫叶的光学观察以及数值模型和矢量分析的展开模拟，发现折痕间距比(a^*)大于1是导致枫叶V形展开的主要原因，而枫叶的折线间距比(a^*)约等于1.4。研究二是对扇形波纹状枫叶展开方式的研究。在此基础上，建立了多个叶片展开的数值模型，模拟了枫叶的扇形展开。通过向量分析得到展开过程中叶片元素的位置和折痕的位置。通过测量和观察发现，当叶片完全折叠时，叶脉之间有1°~2°的小角度间隙。这可能是为了避免由于相对较厚的静脉重叠而导致的局部体积的增加。为了考察卷叶的展开方式，我们以蝴蝶叶为研究对象。作为第一步，利用光学装置测量了蝴蝶叶的形状，如叶脉夹角和叶片厚度。研究发现，蝴蝶叶的叶脉具有椭圆形的横截面，而不是圆形的横截面，无论其大小如何，都具有类似的几何形状。利用叶脉和叶片的几何数据和力学性能，建立了多个叶片模型，并进行了有限元分析。结果表明，脉型最接近的叶型模型对真实蝴蝶叶的承载能力大于其他简化叶型模型。

One of the research in this project is to reveal the unfolding manner of regularly corrugated simple leaves paying attention to the difference between leaf shapes during unfolding of hornbeam and common alder, i.e.a relatively flat shape in hornbeam and a V-shape in common alder leaves. From the optical observation of their leaves and the unfolding simulation using numerical models and vector analysis, it was found that the crease interval ratio(a^*)larger than 1, which is a^*【approximately equal】1.4 in common alder leaves, causes the V-shape unfolding.The second research is to investigate of the unfolding manner of maple leaves which have a fan-type bellows pattern. Based on the measurements, a number of numerical leaf unfolding models were constructed to simulate the fan-type unfolding like maple leaves. The locations of the leaf elements and the creases during unfolding were obtained by vector analysis. From the measurements and observations, it was found that there are small angular gaps of 1°〜2° between the veins when the leaf is fully folded. This may be for avoiding an increase in local volume due to the overlapping of relatively thick veins. These small angular gaps are quite advantageous to compact folding.In order to examine the unfolding manner of rolled leaves, we took butterbur leaves as a target to research. As the first step, the configuration of butterbur leaves, e.g.the angle between veins and the thickness of lamina, was measured using optical devices. It was found that butterbur leaves have veins with an ellipse cross-section instead of a circle cross-section and analopgous geometry irrespective of their size. By using the geometrical data and mechanical properties of veins and a lamina, a number of leaf models were made for FEM analysis. It was found that the capability for supporting load of the leaf model with the most similar venation pattern to a real butterbur leaf was greater than that of other models with simplified patterns.