Homogenization of a System of Elastic and Reaction-diffusion Equations Modelling Plant Cell Wall Biomechanics

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 reactiondiffusion 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. Received November 3rd, 2014. Revised July 30, 2015. Published online March 21, 2016.