  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.
