The study of creeping flow in fibrous media is of considerable interest in many biological and biomedical applications. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today’s high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flow parallel and perpendicular to a single fiber or an array thereof, using a volume averaging theory, were compared to the detailed analysis.
In-plane and out-of-plane stiffness of 2D random fiber networks: Micromechanics and non-classical stiffness relation