Asymptotic expansion homogenization of permeability tensor for plain woven fabrics

Homogenization method is adopted to predict the permeability tensor for glass fiber plain woven fabrics. Numerical calculation of the permeability tensor is an encouraging task because the permeability tensor is a key parameter in resin transfer molding (RTM). Based on multi-scale approach of the homogenization method, permeability of the micro-unit cell for the fiber tow is computed and compared with that obtained from flow analysis for the same micro-unit cell. In order to calculate the permeability tensor of macro-unit cell for the plain woven fabrics, the Stokes and Brinkman equations which describe inter-tow and intra-tow flows, respectively, are employed as governing equations. The effective permeabilities homogenized by considering intra-tow flow are compared with those obtained experimentally. Control volume finite element method (CVFEM) is used as a numerical method. It is shown that the asymptotic expansion homogenization method is an attractive tool to predict the effective permeability for heterogeneous media.