A finite strain fibre-reinforced viscoelasto-viscoplastic model of plant cell wall growth

A finite strain fibre-reinforced viscoelasto-viscoplastic model implemented in a finite element (FE) analysis is presented to study the expansive growth of plant cell walls. Three components of the deformation of growing cell wall, i.e. elasticity, viscoelasticity and viscoplasticity-like growth, are modelled within a consistent framework aiming to present an integrative growth model. The two aspects of growth—turgor-driven creep and new material deposition—and the interplay between them are considered by presenting a yield function, flow rule and hardening law. A fibre-reinforcement formulation is used to account for the role of cellulose microfibrils in the anisotropic growth. Mechanisms in in vivo growth are taken into account to represent the corresponding biologycontrolled behaviour of a cell wall. A viscoelastic formulation is proposed to capture the viscoelastic response in the cell wall. The proposed constitutive model provides a unique framework for modelling both the in vivo growth of cell wall dominated by viscoplasticity-like behaviour and in vitro deformation dominated by elastic or viscoelastic responses. A numerical scheme is devised, and FE case studies are reported and compared with experimental data

Application of the effective formula of growth functional to quantitative description of growth of plant cells

An effective formula describing expansive plant growth is derived from the modified Lockhart/Ortega-type equation. Its applicability is demonstrated on selected experimental data extracted from available literature. Quantitative information about the “diffusion rate” (k 2) of the growth factors is obtained for two different model species in plant science: Arabidopsis thaliana L. belongs to the dicots and Zea mays L. belongs to the monocots. It is shown that the value of the diffusion rate may be useful in comparing different datasets and serve as a measure of reproducibility of standard measurements. Analysis of the formula and fits allows to identify and suggest a set of criteria for reporting future experiments, which would improve comparability and reproducibility of the results