Modelling cell wall growth using a fibre-reinforced hyperelastic–viscoplastic constitutive law

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Huang, R. and Becker, A. A. and Jones, I. A. (2012) Modelling cell wall growth using a fibre-reinforced hyperelastic–viscoplastic constitutive law. Journal of the Mechanics and Physics of Solids, 60 (4). pp. 750-783. ISSN 0022-5096 (https://doi.org/10.1016/j.jmps.2011.12.003)

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Abstract

A fibre-reinforced hyperelastic–viscoplastic model using a finite strain Finite Element (FE) analysis is presented to study the expansive growth of cell walls. Based on the connections between biological concepts and plasticity theory, e.g. wall-loosening and plastic yield, wall-stiffening and plastic hardening, the modelling of cell wall growth is established within a framework of anisotropic viscoplasticity aiming to represent the corresponding biology-controlled behaviour of a cell wall. In order to model in vivo growth, special attention is paid to the differences between a living cell and an isolated wall. The proposed hyperelastic–viscoplastic theory provides a unique framework to clarify the interplay between cellulose microfibrils and cell wall matrix and how this interplay regulates sustainable growth in a particular direction while maintaining the mechanical strength of the cell walls by new material deposition. Moreover, the effect of temperature is taken into account. A numerical scheme is suggested and FE case studies are presented and compared with experimental data.

ORCID iDs

Huang, R. ORCID logoORCID: https://orcid.org/0000-0001-5299-2281, Becker, A. A. and Jones, I. A.;
CORE (COnnecting REpositories)