Homogenization of biomechanical models for plant tissues
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https://hdl.handle.net/10037/12526Date
2017Type
Journal articleTidsskriftartikkel
Peer reviewed
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-diffusion-convection 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 a 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.
Read More: http://epubs.siam.org/doi/10.1137/15M1046198
Description
OA, publishers version allowed institutional repository under the Creative Commons Attribution 4.0 International (CC BY) License
Link to publishers version: https://doi.org/10.1137/15M1046198