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

Homogenization of biomechanical models of plant tissues with randomly distributed cells