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

Huang, Ruoyu; Becker, Adib A.; Jones, I. Arthur

Abstract

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.

Citation

Huang, R., Becker, A. A., & Jones, I. A. (2015). A finite strain fibre-reinforced viscoelasto-viscoplastic model of plant cell wall growth. Journal of Engineering Mathematics, 95(1), https://doi.org/10.1007/s10665-014-9761-y

• Journal Article Type: Article
• Acceptance Date: Oct 29, 2014
• Online Publication Date: Nov 27, 2015
• Publication Date: Dec 3, 2015
• Deposit Date: Jul 28, 2016
• Publicly Available Date: Jul 28, 2016
• Journal: Journal of Engineering Mathematics
• Print ISSN: 0022-0833
• Electronic ISSN: 1573-2703
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 1
• DOI: https://doi.org/10.1007/s10665-014-9761-y
• Keywords: Biological material; Cell wall growth; Constitutive behaviour; Fibre-reinforced composite material; Finite strain; Finite element analysis; Viscoplastic material
• Public URL: https://nottingham-repository.worktribe.com/output/770298
• Publisher URL: http://link.springer.com/article/10.1007%2Fs10665-014-9761-y
• Contract Date: Jul 28, 2016