Microstructure-based evaluation of the influence of woven architecture on permeability by asymptotic homogenization theory

A microstructure-based computational approach is taken to predict the permeability tensor of woven fabric composites, which is a key parameter in resin transfer moulding (RTM) simulation of polymer-matrix composites. An asymptotic homogenization theory is employed to evaluate the permeability from both macro- and microscopic standpoints with the help of the finite-element method (FEM). This theory allows us to study the relation between microscopic woven architecture and macroscopic permeability based on the method of two-scale asymptotic expansions. While the fluid velocity is introduced for Stokes flow microscopically, the macroscopic one is for seepage flow with the Darcy's law. The latter can be characterized for arbitrary configurations of unit microstructures that are analyzed for the former under the assumption of the periodicity. After discussing the validity of this approach, we present a typical numerical example to discuss the permeability characteristics of plain weave fabrics undergoing shear deformation in the preforming in comparison with the underformed one. Another notable feature of the proposed method is that the correlation between the macroscopic behaviors and the microscopic ones can be analyzed, which is important to analyze and/or design the RTM process. Hence, it is also demonstrated that the microscopic velocity field evaluated with macroscopic pressure gradient provides important information about the flow in RTM processes.