How wind drives the correlation between leaf shape and mechanical properties

From a geometrical point of view, a non-sessile leaf is composed of two parts: a large flat plate called the lamina, and a long beam called the petiole which connects the lamina to the branch/stem. While wind is exerting force (e.g. drag) on the lamina, the petiole undergoes twisting and bending motions. To survive in harsh abiotic conditions, leaves may have evolved to form in different shapes, resulting from a coupling between the lamina geometry and the petiole mechanical properties. In this study, we measure the shape of laminae from 120 simple leaf species (no leaflets). Leaves of the same species are found to be geometrically similar regardless of their size. From tensile/torsional tests, we characterize the bending rigidity (EI) and the twisting rigidity (GJ) of 15 petioles of 4 species in the Spring/Summer: Red Oak (Quercus Rubra), American Sycamore (Platanus occidentalis), Yellow Poplar (Liriodendron tulipifera), and Sugar Maple (Acer saccharum). A twist-to-bend ratio EI/GJ is found to be around 4.3, within the range in previous studies conducted on similar species (EI/GJ = 2.7 similar to 8.0 reported in S. Vogel, 1992). In addition, we develop a simple energetic model to find a relation between geometrical shapes and mechanical properties (EI/GJ = 2L(L)/W-C where L-L is the laminar length and W-C is the laminar width), verified with experimental data. Lastly, we discuss leaf's ability to reduce stress at the stem-petiole junction by choosing certain geometry, and also present exploratory results on the effect that seasons have on the Young's and twisting moduli.