Homogenization of Biomechanical Models for Plant Tissues

Andrey Piatnitski (Lead / Corresponding author), Mariya Ptashnyk (Lead / Corresponding author)

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Abstract

In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusionconvection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. The chemical process in cells and the elastic properties of cell walls and middle lamella are coupled because elastic moduli depend on densities involved in chemical reactions, whereas chemical reactions depend on mechanical stresses. Using homogenization techniques we derive rigorously macroscopic model for plant biomechanics. To pass to the limit in the nonlinear reaction terms, which depend on elastic strain, we prove the strong two-scale convergence of the displacement gradient and velocity field.
Original languageEnglish
Pages (from-to)339-387
Number of pages49
JournalMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume15
Issue number1
Early online date9 Nov 2016
DOIs
Publication statusPublished - 2017

Keywords

  • Homogenization
  • Two-scale convergence
  • Periodic unfolding method
  • Poroelasticity
  • Stokes system
  • Biomechanics of plant tissues

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