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

R. Huang, A.A. Becker# & I.A. Jones

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.

Journal of the Mechanics and Physics of Solids 60 (4), 750-783

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