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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.
|Number of pages||39|
|Journal||Esaim: Mathematical Modelling and Numerical Analysis|
|Early online date||21 Mar 2016|
|Publication status||Published - 21 Mar 2016|
- Plant modelling
- Two-scale convergence
- Periodic unfolding method
- Reaction-diffusion equations
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