This paper describes a study of petiole structural morphology in which tissue materials, cross-sectional geometry, layer-architecture and hydrostatic condition are variables that affect the overall structural properties of the organ. Philodendron melinonii is selected as a model species for characterizing the mechanical properties of the petiole. The shape of the petiole is modeled through the polar parameterization of the Lame's curves, i.e. Gielis formulation. A multiscale model of bending stiffness is proposed to capture the impact of changing the constituent tissues and the cross-sectional geometry. Stiffness and density of different tissues are used to plot the domain bounded by the limiting curve of the respective tissue material. Shape parameters and the respective tissue properties are used to generate structural efficiency maps displaying property domains within which fall all possible combinations of tissues that are shaped into a certain geometry during growth. The turgor pressure is also taken into account to show how the domain of the effective material properties changes with water content. Finite element analysis besides experimental data is used to validate the theoretical results. The maps may offer a source of inspiration for biomimetic design, as they help to gain insight into the efficiency of biological beams described by different tissues properties, geometry and turgidity.

Plant petioles and stems are hierarchical cellular structures, displaying structural features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues, in which the cellular distribution is quasirandom. The current work focuses on the realistic modeling of plant tissue microstructures. The finite-edge centroidal Voronoi tessellation (FECVT) is here introduced to overcome the drawbacks of the semi-infinite edges of a typical Voronoi model. FECVT can generate a realistic model of a tissue microstructure, which might have finite edges at its border, be defined by a boundary contour of any shape, and include complex heterogeneity and cellular gradients. The centroid-based Voronoi tessellation is applied to model the microstructure of the Philodendron melinonii petiole and the Arabidopsis thaliana stem, which both display intense cellular gradients. FECVT coupled with a digital image processing algorithm is implemented to capture the nonperiodic microstructures of plant tissues. The results obtained via this method satisfactorily obey the geometric, statistical, and topological laws of naturally evolved cellular solids. The predicted models are also validated by experimental data.

Plant petioles can be considered as hierarchical cellular structures, displaying geometric features defined at multiple length scales. Their macroscopic mechanical properties are the cumulative outcome of structural properties attained at each level of the structural hierarchy. This work appraises the compliance of a rhubarb stalk by determining the stalk's bending and torsional stiffness both computationally and experimentally. In our model, the irregular cross-sectional shape of the petiole and the layers of the constituent tissues are considered to evaluate the stiffness properties at the structural level. The arbitrary shape contour of the petiole is generated with reasonable accuracy by the Gielis superformula. The stiffness and architecture of the constituent layered tissues are modeled by using the concept of shape transformers so as to obtain the computational twist-to-bend ratio for the petiole. The rhubarb stalk exhibits a ratio of flexural to torsional stiffness 4.04 (computational) and 3.83 (experimental) in comparison with 1.5 for isotropic, incompressible, circular cylinders, values that demonstrate the relative structural compliance to flexure and torsion.

Plant petioles and stems are hierarchical cellular structures, displaying geometrical features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues in which the cellular distribution is quasi-random, a factor that affects the elastic properties of the tissues. The current work focuses on the finite element analysis (FEA) of the constituent tissues of the plant Rheum rhabarbarum (rhubarb). The geometric model is generated via a recently introduced method: the finite edge centroidal Voronoi tessellation (FECVT), which is capable to capture the gradients of cellularity and diversified pattern of cellular materials, as opposed to current approaches in literature. The effective stiffness of the tissues is obtained by using an accurate numerical homogenization technique via detailed finite element analysis of the models of sub-regions of the tissues. As opposed to a large-scale representative volume element (RVE), statistical volume elements (SVE) are considered in this work to model tissue microstructures that are highly random. 2D finite element analyses demonstrate that the distribution of cells in collenchyma and parenchyma tissue make them stiffer in two different directions, while the overall effect of the combined tissues results in approximately equal stiffness in both directions. The rhubarb tissues, on the other hand, are more compliant than periodic and quasi-uniform random cellular materials by a factor of up to 47% and 44%, respectively. The variations of the stiffness shows the stiffening role that cell shape, size, and graded cellular distribution play in the mechanics of the rhubarb tissue.