Deformation dependent permeability from variationally consistent homogenization

Abstract

In this article, the influence of large deformations on the effective permeability of a bicontinuous porous material is investigated. On the fine-scale, Neo–Hooke hyperelasticity is considered for the solid skeleton. In a third medium approach, we model the pore space as filled with a softer material of the same type. Fluid flow through the deformed pores is expressed in terms of a Stokes' flow model. The influence of the pore pressure on the deformation is neglected, resulting in a one-way coupling which allows for a sequential solution of the two physical problems. The framework of Variationally Consistent Homogenization is used to derive a two-scale formulation based on a Representative Volume Element (RVE) characterizing the microstructure. Finally, a two-step procedure to compute the deformation dependent permeability is established: Firstly, the deformation of the RVE for a given macroscale deformation gradient is computed. Secondly, sensitivities for the fluid flow through the deformed RVE are computed and used to determine the effective permeability tensor. A numerical study is conducted for sets of RVEs with the same material parameters and different porosity. For the case of uniaxial compression, a significant influence of the deformation on the effective permeability is observed: For a macroscale compression of $20\%$, the effective permeability orthogonal to the compression direction is reduced by almost $60\%$.