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.

中文翻译：

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具有随机分布细胞的植物组织生物力学模型的均质化

在本文中，考虑了具有随机分布细胞的植物组织的生物力学数学模型的均质化。植物组织的机械特性由用于植物细胞和细胞壁化学过程的反应-扩散-对流方程的强耦合系统、植物细胞壁和中层弹性变形的多孔弹性方程以及用于细胞内的流体流动。力学和化学之间的非线性耦合是由植物组织的弹性特性对化学物质密度的依赖性以及化学反应对存在于组织中的机械应力的依赖性给出的。使用随机均质化技术，我们推导出具有随机细胞分布的植物组织生物力学的严格宏观模型。强随机两尺度收敛被证明达到非线性反应项的极限。引入边界项的适当含义，在微观尺度上定义具有通量边界条件和传输条件的宏观方程。