Homogenization of biomechanical models for plant tissues

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.

References in corpus (2)

• Modeling semiflexible polymer networks
• Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach

Cited by in corpus (4)

• Homogenization of biomechanical models of plant tissues with randomly distributed cells
• Stochastic unfolding and homogenization of spring network models
• Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations
• Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization