Effect of Crease Interval on Unfolding Manner of Corrugated Tree Leaves

In this study, the unfolding of corrugated simple leaves such as hornbeam or common alder leaves, was observed. Based on the observation, a series of numerical models with various crease interval ratios, a^* (=a_2 / a_1, a_1:the distance from a valley crease to a crest crease, a_2:the distance from a crest crease to a valley crease) were considered to investigate the effect of a^* on the unfolding manner of corrugated leaves. By using vector analysis and transformation of coordinates with the models, numerical simulatioins for the unfolding of corrugated leaves were performed. A number of characteristic values such as angles between lamina elements and the movements of creases (valley creases run along main veins) were calculated during unfolding. The relationship between a^* and the kinetic energy of leaves during unfolding was also examined. It was found that the difference in unfolding manner between hornbeam and common alder leaves may be caused by the difference in the crease interval ratio in a leaf, a^*, i.e., a^* ≈ 1.0 in hornbeam leaves and a^* ≈ 1.3 in common alder leaves. It can be understood that hornbeam leaves with a relatively small vein diameter could choose a^*=1.0 to reduce the volume of fully folded leaves, while common alder leaves with a large vein diameter had to choose a value of a^*≠1.0 to avoid the increase in local volume due to the overlap of veins.