Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics

Ptashnyk, Mariya; Seguin, Brian

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 2, pp. 593-631.

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.

Classification : 35B27, 35Q92, 35Kxx, 74Qxx, 74A40, 74D05
Mots clés : Homogenization, two-scale convergence, periodic unfolding method, elasticity, reaction-diffusion equations, plant modelling

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