Computational homogenization for two-scale modeling of perfused tissues

Abstract

We developed a two-scale approach for modeling large-deforming perfused media with the 3-compartment microstructure. An incremental formulation based on the updated Lagrangian configuration and the Biot-type continuum model is introduced. Equations of the model express mechanical equilibrium and the volume fluid redistribution (the Darcy law), assuming both the fluid and solid phases are incompressible. This linearized system was treated by the homogenization method assuming locally periodic structures. The local reference cell involving geometrical representations of the blood vessels evolves in time due to large deformation. The homogenized model is implemented using a finite element code and a numerical example is presented.