Abstract
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.
Original language | English |
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Pages (from-to) | 593-631 |
Number of pages | 39 |
Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
Volume | 50 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 2016 |
Keywords
- Elasticity
- Homogenization
- Periodic unfolding method
- Plant modelling
- Reaction-diffusion equations
- Two-scale convergence
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics
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Mariya Ptashnyk
- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Mathematics - Associate Professor
Person: Academic (Research & Teaching)