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

A step towards new irrigation scheduling strategies using plant-based measurements and mathematical modelling

Because of the increasing worldwide shortage of freshwater and costs of irrigation, a new plant-based irrigation scheduling method is proposed. In this method, two real-time plant-based measurements (sap flow and stem diameter variations) are used in combination with a mathematical water flow and storage model in order to predict the stem water potential. The amount of required irrigation water is derived from a time integration of the sap flow profile, while the timing of the irrigation is controlled based on a reference value for the predicted stem water potential. This reference value is derived from the relationship between midday values of maximum photosynthesis rates and stem water potential. Since modelling is an important part of the proposed methodology, a thorough mathematical analysis (identifiability analysis) of the model was performed. This analysis showed that an initial (offline) model calibration was needed based on measurements of sap flow, stem diameter variation and stem water potential. Regarding irrigation scheduling, however, only sap flow and stem diameter variation measurements are needed for online simulation and daily model calibration. Model calibration is performed using a moving window of 4 days of past data of stem diameter variations. The research tool STACI (Software Tool for Automatic Control of Irrigation) was used to optimally combine the continuous measurements, the mathematical modelling and the real-time irrigation scheduling. The new methodology was successfully tested in a pilot-scale setup with young potted apple trees (Malus domestica Borkh) and its performance was critically evaluated