Homogenization of a viscoelastic model for plant cell wall biomechanics

Mariya Ptashnyk, Brian Seguin

Research output: Contribution to journalArticle

130 Downloads (Pure)

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 (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.
Original languageEnglish
Pages (from-to)1447-1471
Number of pages26
JournalESAIM: Control, Optimisation and Calculus of Variations
Volume23
Issue number4
Early online date1 Sep 2016
DOIs
Publication statusPublished - Oct 2017

Fingerprint

Viscoelastic Model
Biomechanics
Cell Wall
Homogenization
Cells
Viscoelasticity
Elastic deformation
Ordinary differential equations
Linear Viscoelasticity
Cellulose
Two-scale Convergence
Memory Term
Plant Cells
Elastic Deformation
Chemical Processes
Reaction-diffusion
Unfolding
Data storage equipment
Governing equation
Ordinary differential equation

Keywords

  • Homogenization
  • two-scale convergence
  • periodic unfolding method
  • viscoelasticity
  • plant modelling

Cite this

@article{57ea6b82197348258496da61512adbcf,
title = "Homogenization of a viscoelastic model for plant cell wall biomechanics",
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 (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.",
keywords = "Homogenization, two-scale convergence, periodic unfolding method, viscoelasticity, plant modelling",
author = "Mariya Ptashnyk and Brian Seguin",
note = "M. Ptashnyk and B. Seguin gratefully acknowledge the support of the EPSRC First Grant EP/K036521/1 “Multiscale modelling and analysis of mechanical properties of plant cells and tissues”.",
year = "2017",
month = "10",
doi = "10.1051/cocv/2016060",
language = "English",
volume = "23",
pages = "1447--1471",
journal = "ESAIM: Control, Optimisation and Calculus of Variations",
issn = "1292-8119",
publisher = "EDP Sciences",
number = "4",

}

Homogenization of a viscoelastic model for plant cell wall biomechanics. / Ptashnyk, Mariya; Seguin, Brian.

In: ESAIM: Control, Optimisation and Calculus of Variations, Vol. 23, No. 4, 10.2017, p. 1447-1471.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Homogenization of a viscoelastic model for plant cell wall biomechanics

AU - Ptashnyk, Mariya

AU - Seguin, Brian

N1 - M. Ptashnyk and B. Seguin gratefully acknowledge the support of the EPSRC First Grant EP/K036521/1 “Multiscale modelling and analysis of mechanical properties of plant cells and tissues”.

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

KW - Homogenization

KW - two-scale convergence

KW - periodic unfolding method

KW - viscoelasticity

KW - plant modelling

U2 - 10.1051/cocv/2016060

DO - 10.1051/cocv/2016060

M3 - Article

VL - 23

SP - 1447

EP - 1471

JO - ESAIM: Control, Optimisation and Calculus of Variations

JF - ESAIM: Control, Optimisation and Calculus of Variations

SN - 1292-8119

IS - 4

ER -