Geodesic
Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics
Ptashnyk, Mariya1 ; Seguin, Brian1
1 Division of Mathematics, University of Dundee Dundee, DD1 4HN, UK.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 2, pp. 593-631

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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.

DOI : 10.1051/m2an/2015073
Classification : 35B27, 35Q92, 35Kxx, 74Qxx, 74A40, 74D05
Keywords: Homogenization, two-scale convergence, periodic unfolding method, elasticity, reaction-diffusion equations, plant modelling

Ptashnyk, Mariya 1 ; Seguin, Brian 1

1 Division of Mathematics, University of Dundee Dundee, DD1 4HN, UK. 
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Ptashnyk, Mariya; Seguin, Brian. Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 2, pp. 593-631. doi: 10.1051/m2an/2015073

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