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

R. Huang*, A. A. Becker, I. A. Jones

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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 biology-controlled 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.
Original languageEnglish
Pages (from-to)121-154
Number of pages34
JournalJournal of Engineering Mathematics
Volume95
Early online date27 Nov 2015
DOIs
Publication statusPublished - 30 Dec 2015

Keywords

  • biological material
  • cell wall growth
  • constitutive behaviour
  • fibre-reinforced composite material
  • finite strain
  • finite element analysis
  • viscoplastic material

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