| Issue |
ESAIM: M2AN
Volume 50, Number 2, March-April 2016
|
|
|---|---|---|
| Page(s) | 593 - 631 | |
| DOI | https://doi.org/10.1051/m2an/2015073 | |
| Published online | 21 March 2016 | |
Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics∗
Division of Mathematics, University of Dundee Dundee, DD1 4HN, UK.
mptashnyk@maths.dundee.ac.uk; m.ptashnyk@dundee.ac.uk; bseguin@maths.dundee.ac.uk
Received: 3 November 2014
Revised: 30 July 2015
In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a cell wall coming from the cellulose microfibrils and the chemical reactions between the cell wall’s constituents. Particular attention is paid to the role of pectin and the impact of calcium-pectin cross-linking chemistry on the mechanical properties of the cell wall. We prove the existence and uniqueness of the strongly coupled microscopic problem consisting of the equations of linear elasticity and a system of reaction-diffusion and ordinary differential equations. Using homogenization techniques (two-scale convergence and periodic unfolding methods) we derive a macroscopic model for plant cell wall biomechanics.
Mathematics Subject Classification: 35B27 / 35Q92 / 35Kxx / 74Qxx / 74A40 / 74D05
Key words: Homogenization / two-scale convergence / periodic unfolding method / elasticity / reaction-diffusion equations / plant modelling
© EDP Sciences, SMAI 2016
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