Modelling The Micro- And Macro-structure Efficiencies Of A Compliant Petiole Beam
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107 - 117
Structural geometry and material properties govern the way in which a petiole complies to wind and gravity forces. Earlier works that examined the mechanical efficiency of a petiole undergoing twisting and bending proposed simplified models for its geometry and material. The former was approximated with a theoretical semi-elliptical contour, while the latter was viewed as a homogeneous material. These simplifications are refined in this paper, which presents progress on both issues. The petiole is considered as a hierarchical structure with differently sized structural features. A multiscale model of the twist to bend ratio is presented to capture the structural efficiencies of the petiole at both the macro- and micro-scale. Dimensionless factors and shape parameters are introduced to describe the coupling effect of the efficiency gained at different levels of the length scale. The results are plotted into efficiency maps showing how structural hierarchies impact the compliant properties of a petiole beam. Keywords: microstructure, structural hierarchy, shape, twist to bend ratio. 1 Introduction A leaf petiole can be considered as a hierarchical solid that contains structural features at different length scales. Cellulose is the material building block, which is shaped during growth into several structural hierarchies. At each hierarchical level, the elements repeat themselves to form ordered patterns. The architecture of these patterns and the way in which they are nested into each other plays a crucial role in the overall mechanical responses of the petiole. Flexibility is a property each plant possesses to varying degrees and specific to each species. As other motile and sessile organisms, leaf petioles exhibit the ability to adjust their posture in response to applied external forces. Flexibility is
microstructure, structural hierarchy, shape, twist to bend ratio.