Homogenization of biomechanical models for plant tissues

TL;DR

This paper develops a rigorous multiscale model for plant tissue biomechanics by homogenizing a complex coupled system of chemical, elastic, and fluid flow equations, capturing interactions across microscopic and macroscopic scales.

Contribution

It introduces a novel homogenization approach for a strongly coupled reaction-diffusion, poroelasticity, and fluid flow system in plant tissues, deriving a comprehensive macroscopic model.

Findings

Derived a macroscopic model for plant biomechanics

Proved strong two-scale convergence of key variables

Established coupling effects between chemical and mechanical processes

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.