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

本项目的研究之一是揭示规则波纹单叶的展开方式，注意角木和普通桤木展开过程中叶片形状的差异，即角木的相对平坦形状和普通桤木的V形形状。通过叶片的光学观察和数值模型及矢量分析的展开模拟，发现常见桤木叶片的褶皱间隔比（a^*）大于1（a^* 约等于1.4）时，会导致V形展开。在此基础上，建立了一系列数值叶片展开模型，模拟了叶片的扇形展开。通过矢量分析获得了展开过程中叶元素和折痕的位置。从测量和观察中发现，当叶子完全折叠时，脉之间存在1°至2°的小角度间隙。这可以是为了避免由于相对厚的静脉的重叠而导致的局部体积的增加。为了考察卷叶的展开方式，我们以款冬叶为研究对象。首先，利用光学仪器测量款冬叶片的形态，如脉间夹角和叶片厚度。结果表明，款冬叶片的叶脉横截面为椭圆形，而不是圆形，无论大小，其几何形状都类似。利用叶片的几何数据和力学特性，建立了叶片的有限元模型。结果表明，与真实的款冬叶片脉型最相似的叶片模型的承载能力大于其他简化模型。

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.