LAUSR

Abstract 2D and 3D numerical permeability of fibrous media are studied based on Stokes and Stokes-Darcy flows simulated by a Finite Element Modelling (FEM). A monolithic approach stabilised by an Algebraic Sub-Grid Scale (ASGS) method and implemented in a FEM software (Z-set) is used. The 2D geometries have been generated according to ideal arrangements and 3D geometry are representative of a highly anisotropic ply-to-ply interlock unit cell. For both geometries, yarns have been first considered as impermeable, and then the same calculations have been conducted with various intra-yarn permeabilities. The main novelty of this work is to address the dual-scale permeability problem with a Stokes-Darcy modelling so as to override numerical strategy robustness issues. An empirical law has been proposed to link the effective permeability to the intra-yarn one : this allows to generalise previously established results to real 3D materials with complex structures. An intra-yarn permeability threshold (asymptotic value) from which yarns can be considered impermeable has also been highlighted. This study underlines the importance of unit cell definition when it comes to computing permeability of 3D structures numerically generated, especially non-periodicity issues. Two methods to decrease the impact of preferential flows are then discussed.