Deformation-dependent permeability of fibrous materials

Fluid flow in fibrous materials depends on volumetric deformation, distortional deformation and fibre reorientation. The latter two effects introduce anisotropy in the hydraulic permeability. Motivated by the study of biological tissues, this work aims to develop an analytical model for evaluating the deformation-dependent permeability of fibrous materials. The material consists of a three-dimensional assembly of long fibres of a single type, with the fluid flowing through the interstices between the fibres. The macroscopic deformations are related to the deformation of a cylindrical representative element of volume (REV), comprised of a fibre surrounded by a cylindrical jacket of fluid. The effect of fibre orientation is modelled using an orientational probability distribution function (OPDF), and the REV permeability tensor is then evaluated using previously developed methods, accounting for the macroscopic deformation. Finally, the overall permeability tensor is calculated via directional averaging of the REV permeability tensor, in which the fibre OPDF serves as the weighing function. The model is validated numerically via a uniaxial contraction (confined compression) test performed for the case of an OPDF that is isotropic in the reference (undeformed) configuration, and is found to qualitatively reproduce experimental findings. The proposed model offers an analytical tool for evaluating the permeability of fibrous materials under large deformations, based on structural information such as fibre volumetric fraction, diameter and spatial orientation.