Finite element modelling of complex movements during self-sealing of ring incisions in leaves of Delosperma cooperi

Abstract

A numerical computer model was developed in order to describe the complex self-sealing mechanism of injured Delosperma cooperi leaves. For this purpose, the leaf anatomy was simplified to a model consisting of five concentric tissue layers. Specific parameters (modulus of elasticity, permeability, porosity, etc.) were assigned to each tissue type for modelling its physical properties. These parameters were either determined experimentally from living plant material or taken from literature. The developed computer model considers the leaf as a liquid-filled porous body within a continuum approach in order to determine the governing equations. The modelling of the wound accounts for both the injury of peripheral tissues and the free surfaces caused by the incision. The loss of water through these free surfaces initiates the self-sealing process. It is further shown that the tissue permeability and the reflection coefficient (relative permeability of a cell membrane for solutes) are the determining parameters of the self-sealing process, whereas the modulus of elasticity has a negligible influence. Thus, the self-sealing mechanism is a hydraulically driven process which leads to a local (incision region) and global (total leaf) contraction of the leaf. The accuracy of the modelled self-sealing process was validated by comparing simulation results with experiments conducted on natural plant leaves. The results will serve as valuable input for developing novel, bio-inspired technical products with self-sealing function.

Keywords: Delosperma; Hydraulic movement; Numerical simulation; Reflection coefficient; Self-sealing.