HOMOGENIZATION OF A SYSTEM OF ELASTIC AND REACTION-DIFFUSION EQUATIONS MODELLING PLANT CELL WALL BIOMECHANICS

作者：Ptashnyk Mariya^*; Seguin Brian^*

来源：Esaim: Mathematical Modelling and Numerical Analysis , 2016, 50(2): 593-631.

DOI：10.1051/m2an/2015073

• Homogenization
• two-scale convergence
• periodic unfolding method
• elasticity
• reaction-diffusion equations
• plant modelling

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.

• 出版日期2016-4