A unified approach to hyperelastic modelling of plant cell walls

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Huang, Ruoyu (2025) A unified approach to hyperelastic modelling of plant cell walls. Mathematics and Mechanics of Solids, 30 (11). pp. 2574-2618. ISSN 1081-2865 (https://doi.org/10.1177/10812865251350689)

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Abstract

The structure of the microfibrils network poses the key challenge to understand not only the mechanical behaviours but also the growth mechanisms of the plant cell wall. A number of competing hypotheses with contradictory assumptions, including the recently proposed contact model and the more conventional tethering model, have been proposed to address the challenge. In the present study, a fibre-reinforced hyperelastic model is proposed aiming to cover both the contact model and the tethering model in a unified mathematical framework. A variety of anisotropies, including those arising from the moiré pattern and the contacts, are taken into account. The formulation is presented in terms of the principal stretches for more direct correlation with the biological experimental observations. The details of the stresses and tangent moduli are provided for readily implementing in finite-element modelling. The simple shear problem is studied to provide the quantitative insight into the long-term biological hypothesis that cell wall growth is driven by shear deformations. The moiré pattern under tensile stretch is demonstrated. The local motion of microfibrils is examined by using rod theory. A corresponding potential growth mode is proposed with the analysis using Burgers vector and torsion in material space.

ORCID iDs

Huang, Ruoyu ORCID logoORCID: https://orcid.org/0000-0001-5299-2281;
CORE (COnnecting REpositories)