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A Multiscale Mechanical Model for Plant Tissue Stiffness
Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. W., Montreal, QC H3A 0C3, Canada
Department of Chemical Engineering, McGill University, 3610 Rue University, Montreal, QC H3A 0C5, Canada
* Author to whom correspondence should be addressed.
Received: 1 April 2013; in revised form: 10 May 2013 / Accepted: 13 May 2013 / Published: 10 June 2013
Abstract: Plant petioles and stems are hierarchical cellular structures, displaying structuralfeatures defined at multiple length scales. The current work focuses on the multi-scalemodelling 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, thecomposition of the cell wall and the structural properties of its constituents. The cell wallis analogous to a fiber reinforced composite, where the cellulose microfibril (CMF) is theload bearing component. For multilayered cell wall, the microfibril angle (MFA) in themiddle layer of the secondary cell wall (S2 layer) largely affects the longitudinal stiffnessfor 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 dicotyledonousplant, 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 beendeveloped and implemented to generate the non-periodic microstructure of the plant tissue.The effective elastic properties of the cellular tissue are obtained through finite elementanalysis (FEA) of the Voronoi model coupled with the cell wall properties. The stiffness ofthe hierarchically modeled tissue is critically important in determining the overall structuralproperties of plant petioles and stems.
Keywords: FECVT; Voronoi; FEA; effective stiffness; cellulose microfibril
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MDPI and ACS Style
Faisal, T.R.; Rey, A.D.; Pasini, D. A Multiscale Mechanical Model for Plant Tissue Stiffness. Polymers 2013, 5, 730-750.
Faisal TR, Rey AD, Pasini D. A Multiscale Mechanical Model for Plant Tissue Stiffness. Polymers. 2013; 5(2):730-750.
Faisal, Tanvir R.; Rey, Alejandro D.; Pasini, Damiano. 2013. "A Multiscale Mechanical Model for Plant Tissue Stiffness." Polymers 5, no. 2: 730-750.