An electric circuit analogy-based homogenization approach for predicting the effective permeability of complex dual-scale porous media

An analogy of electric circuits has been successfully used in this study to formulate models for predicting principle permeability of a dual-scale 3D orthogonal reinforcement. In this novel approach, the 3D complex reinforcement geometry was segregated into regions with uniform permeability and an equivalent circuit diagram was constructed. To accommodate channels of various shapes, the permeability in homogenous regions was computed using the hydraulic resistances concept combined with Darcy's Law. A hierarchical averaging scheme was then employed to estimate the overall effective reinforcement permeability. The permeability values predicted by the models correlated well with the digital flow simulations. The micro-scale permeability was found to be significant only when the overall permeability of the 3D orthogonal fabric was less than 10⁻¹¹ m², below which the overall permeability values bifurcated away from the values computed assuming a solid yarn. The relative difference in the magnitudes of permeability at both meso and micro scales also affects the resin flow patterns within the 3D reinforcement. The formulation presented in this work may provide an alternate route to lengthy experimental and numerical procedures associated with permeability prediction of complex reinforcements and can relate principle permeability to both micro and meso-scale features of any textile reinforcement.