Transversal flow-induced deformation of fibres during composites manufacturing and the effect on permeability

Low Reynolds number flow of a viscous fluid through bundles in non-crimp stitched fabrics is considered for different arrangements of the fibres within the bundles. Using a previous derived model, two-dimensional Navier-Stokes solutions are sampled for the flow between a few fibres with a subsequent minimisation of the dissipation rate in the total system of fibres. Based on the detailed geometry of the fabrics flow induced elastic deformations of the fibre bundles are then derived and the overall permeability is computed for different pressure gradients. The permeability of random arrays of a large number of as well mono-dispersed as poly-dispersed fibres increases as the flow-induced deformation increases and despite the relative shift of the fibres is small the overall change in permeability is essential. For a system with gaps between bundles the change in permeability depends on the orientation of the flow field with respect to the geometry studied while for a regular packing the alteration in permeability is negligible.