Growth spin in plant cell wall growth and remodelling

Abstract

A growth spin model is proposed for the modelling of the expansive growth and fibre remodelling of cell wall. The introduction of the growth spin allows to relax the perfectly bonding assumption in the kinematical growth, which provides a more sophisticated and flexible kinematical description for modelling the selective control and flexible regulation of anisotropic growth. Extended hardening laws are proposed for the growth and remodelling, respectively, aiming at further clarification of the dynamic balance between hardening and softening in a growing cell wall. The proposed model may shed a new light into the micro-structural interpretation of the “fictitious” intermediate (growth) configuration in the kinematical growth modelling of soft matter. A case study of the cell wall as a growing cylindrical wall is presented to demonstrate the proposed model. Spencer’s deviatoric stress tensor and its rate format are shown to play a key role in the modelling of the cell wall as a fibre-reinforced soft tissue.