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.
Keywords: Homogenization, two-scale convergence, periodic unfolding method, elasticity, reaction-diffusion equations, plant modelling
@article{M2AN_2016__50_2_593_0, author = {Ptashnyk, Mariya and Seguin, Brian}, title = {Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {593--631}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/m2an/2015073}, mrnumber = {3482556}, zbl = {1342.35031}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015073/} }
TY - JOUR AU - Ptashnyk, Mariya AU - Seguin, Brian TI - Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 593 EP - 631 VL - 50 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015073/ DO - 10.1051/m2an/2015073 LA - en ID - M2AN_2016__50_2_593_0 ER -
%0 Journal Article %A Ptashnyk, Mariya %A Seguin, Brian %T Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 593-631 %V 50 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015073/ %R 10.1051/m2an/2015073 %G en %F M2AN_2016__50_2_593_0
Ptashnyk, Mariya; Seguin, Brian. Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 2, pp. 593-631. doi : 10.1051/m2an/2015073. http://www.numdam.org/articles/10.1051/m2an/2015073/
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