A Multiscale Model to Determine the Stiffness of Collenchyma Tissue in Rheum Rhabarbarum

Abstract

The stiffness of plant tissue largely influences the overall mechanical response of plant organs, such as stems, branches and leaf petioles. This work examines the structural hierarchy of the plant tissue; in particular of the collenchyma tissue of the Rheum rhabarbarum. The goal of the paper is to develop a multiscale model capturing features of two orders of its structural hierarchy: cell wall and tissue architecture. The former is considered as a fiber reinforced composite, where the cellulose microfibril (CMF) is the main load bearing component. The longitudinal stiffness of the middle (S2) layer of the secondary cell wall is affected by the microfibril angle (MFA) up to 45° to a greater extent, which in turn plays a role in the overall wall stiffness. The latter, i.e. tissue architecture, influences the tissue stiffness through its random distribution of cells. Finite-edge Centroidal Voronoi Tessellation (FECVT) is used to model the non-periodic microstructure of the rhubarb collenchyma, whose effective elastic properties are obtained through finite element analysis. The results from the FECVT model show that the effective stiffness in the longitudinal direction is 15 to 25% higher than that in the transverse direction for relative density between 5 and 30%. The variation reflects the stiffening effect of the shape and size of the cells in the collenchyma tissue, as well as its aperiodic cellular distribution.