Hierarchical Microstructure and Elastic Properties of Leaf Petiole Tissue in Philodendron melinonii
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Hierarchical Microstructure and Elastic Properties of Leaf Petiole Tissue in Philodendron melinonii Tanvir R. Faisal1, Alejandro D. Rey2 and Damiano Pasini1 1 Deparment of Mechanical Engineering, McGill University, Montreal, QC H2A 2K6, CANADA. 2 Department. of Chemical Engineering, McGill University, Montreal, QC H3A 2B2, CANADA. ABSTRACT The leaf petiole is an organ that connects the leaf blade to the stem of a plant. From a structural viewpoint, the petiole resembles a cantilever beam that withstands torsional loading due to wind action and bending deformation due to gravity acting on the leaf blade. During growth, the petiole develops defined structural features at multiple length scales, which synergistically determine its mechanical response to external stimuli. The focus of this study is on the hierarchical level (n=3) of the cellular tissue. The goal is to capture the elastic properties of the cellular tissues of the leaf petiole in Philodendron melinonii at that hierarchy. Since the microstructure of the plant tissues resembles a non-periodic cellular pattern, we resort to a 2-D Finite Edge Centroidal Voronoi tessellation (FECVT) to generate a realistic network of polygonal cells. An analysis based on finite element analysis (FEA) is performed to explore the relation between the effective stiffness of Voronoi model and the properties of the cellular tissue. The effective (homogenized) elastic properties of the cellular tissue can be used to calculate the overall flexural and torsional stiffness of the P. melinonii petiole. The FEA of the Voronoi microstructure depicts the anisotropic stiffness properties of the P. melinonii tissue and its dependence with the graded cellularity. INTRODUCTION The petiole in plants is one of the load bearing structures abundantly available in nature. The petiole is an organ that serves to attach the leaf to the stem. It resembles a cantilever beam that supports the leaf against gravity, exposing it to the sun. It thus provides mechanical support against the weight of the leaf and against environmental factors such as rain and wind, resisting both bending and twisting load [1]. In this work, the petiole of Philodendron melinonii plant (figure 1) has been considered as an example of a cantilever beam that must resist combined loads including bending and twisting. Philodendron melinonii, a terrestrial and epiphytic monocot of the Araceae family, was first discovered in the rain forests of French Guiana, Suriname, Venezuela, and Northern Brazil. The leaves and petioles of P. melinonii can grow quite large, each measuring approximately 28 inches in length. The petiole can be considered a hierarchical cellular structure, having structural features defined at multiple length scales. At each level of the hierarchy, the elements repeat themselves to form ordered patterns. The architecture of the ordered patterns, as well as the nesting of the patterns into each other, makes a vital contribution to the overall mechanical properties of the organ. The P. melinonii petiole shown in figure
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