  In this paper homogenization of a mathematical model for biomechanics of a
plant tissue with randomly distributed cells is considered. Mechanical
properties of a plant tissue are modelled by a strongly coupled system of
reaction-diffusion-convection equations for chemical processes in plant cells
and cell walls, the equations of poroelasticity for elastic deformations of
plant cell walls and middle lamella, and the Stokes equations for fluid flow
inside the cells. The nonlinear coupling between the mechanics and chemistry is
given by the dependence of elastic properties of plant tissue on densities of
chemical substances as well as by the dependence of chemical reactions on
mechanical stresses present in a tissue. Using techniques of stochastic
homogenization we derive rigorously macroscopic model for plant tissue
biomechanics with random distribution of cells. Strong stochastic two-scale
convergence is shown to pass to the limit in the non-linear reaction terms.
Appropriate meaning of the boundary terms is introduced to define the
macroscopic equations with flux boundary conditions and transmission conditions
on the microscopic scale.
