A Multiscale Mechanical Model for Plant Tissue Stiffness

Plant petioles and stems are hierarchical cellular structures, displaying structural features defined at multiple length scales. The current work focuses on the multi-scale modelling of plant tissue, considering two orders of structural hierarchy, cell wall and tissue. The stiffness of plant tissue is largely governed by the geometry of the tissue cells, the composition of the cell wall and the structural properties of its constituents. The cell wall is analogous to a fiber reinforced composite, where the cellulose microfibril (CMF) is the load bearing component. For multilayered cell wall, the microfibril angle (MFA) in the middle layer of the secondary cell wall (S2 layer) largely affects the longitudinal stiffness for values up to 40o. The MFA in turn influences the overall wall stiffness. In this work, the effective stiffness of a model system based on collenchyma cell wall of a dicotyledonous plant, the Rheum rhabarbarum, is computed considering generic MFA and volume fractions. At the cellular level, a 2-D Finite Edge Centroidal Voronoi tessellation (FECVT) has been developed and implemented to generate the non-periodic microstructure of the plant tissue. The effective elastic properties of the cellular tissue are obtained through finite element analysis (FEA) of the Voronoi model coupled with the cell wall properties. The stiffness of the hierarchically modeled tissue is critically important in determining the overall structural properties of plant petioles and stems.