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The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions between viscoelastic deformations of a plant cell wall and chemical processes in the cell wall matrix. We consider elastic deformations of the cell wall microfibrils and viscoelastic Kelvin–Voigt type deformations of the cell wall matrix. Using homogenization techniques (two-scale convergence and periodic unfolding methods) we derive macroscopic equations from the microscopic model for cell wall biomechanics consisting of strongly coupled equations of linear viscoelasticity and a system of reaction-diffusion and ordinary differential equations. As is typical for microscopic viscoelastic problems, the macroscopic equations governing the viscoelastic deformations of plant cell walls contain memory terms. The derivation of the macroscopic problem for the degenerate viscoelastic equations is conducted using a perturbation argument.
Ptashnyk, Mariya 1 ; Seguin, Brian 2
@article{COCV_2017__23_4_1447_0,
author = {Ptashnyk, Mariya and Seguin, Brian},
title = {Homogenization of a viscoelastic model for plant cell wall biomechanics},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1447--1471},
publisher = {EDP-Sciences},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016060},
mrnumber = {3716928},
zbl = {1380.35018},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016060/}
}
TY - JOUR AU - Ptashnyk, Mariya AU - Seguin, Brian TI - Homogenization of a viscoelastic model for plant cell wall biomechanics JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1447 EP - 1471 VL - 23 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016060/ DO - 10.1051/cocv/2016060 LA - en ID - COCV_2017__23_4_1447_0 ER -
%0 Journal Article %A Ptashnyk, Mariya %A Seguin, Brian %T Homogenization of a viscoelastic model for plant cell wall biomechanics %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1447-1471 %V 23 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016060/ %R 10.1051/cocv/2016060 %G en %F COCV_2017__23_4_1447_0
Ptashnyk, Mariya; Seguin, Brian. Homogenization of a viscoelastic model for plant cell wall biomechanics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1447-1471. doi: 10.1051/cocv/2016060
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