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Abstract
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 (twoscale 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 reactiondiffusion 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.
Original language  English 

Pages (fromto)  14471471 
Number of pages  26 
Journal  ESAIM: Control, Optimisation and Calculus of Variations 
Volume  23 
Issue number  4 
Early online date  1 Sept 2016 
DOIs  
Publication status  Published  Oct 2017 
Keywords
 Homogenization
 twoscale convergence
 periodic unfolding method
 viscoelasticity
 plant modelling
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 1 Finished

Multiscale Modelling and Analysis of Mechanical Properties of Plant Cells and Tissues
Ptashnyk, M.
Engineering and Physical Sciences Research Council
1/01/14 → 31/12/15
Project: Research