Analysis of dynamic flows through porous media. Part II: Deformation of a double‐scale fibrous reinforcement

Abstract Porous media are encountered in numerous applications from Soil Mechanics to composite materials manufacturing. Part I of this article investigated the flow behavior in a double‐scale porous medium, i.e., in a material with a bimodal distribution of pore sizes. Typical examples of such medium are the dry fibrous reinforcements used in composite manufacturing through which resin is injected. This type of porous medium contains two types of pores: microscopic voids inside the fiber tows and macroscopic ones between the tows. Because of this double‐scale structure, the saturation of such reinforcing materials is not instantaneous during resin injection. Part I has shown that the notion of saturation must be taken into account in order to describe accurately transient unsaturated flows during the filling of double‐scale fibrous materials. Part II of this investigation is concerned with the transient flow behaviors that can be observed once the reinforcement is saturated. In permanent regime, saturated resin flows are governed by Darcy's law, which describes the purely linear pressure drop observed in fully saturated reinforcements. However, this model cannot be applied to transient saturated flows unless they are considered as a succession of quasi‐stationary flows. Simple macroscopic measurements during transient flow regimes permit us to derive important information on the microscopic characteristics of the flow in connection with the deformations of the porous medium under the effect of fluid pressure. The pressure variations in time observed in permanent flow regimes, when the flow rate is changed, are connected with the double‐scale porosity structure of the fibrous reinforcement. Therefore the second part of this analysis is focused on the stress‐stain behavior of fibrous reinforcements deformed by the pore pressure. A physical model based on Kelvin‐Voigt visco‐elastic material is proposed here to describe the dynamic compaction and relaxation behaviors of saturated fibrous reinforcements. This approach is not only in good agreement with experiments, but it shows also that double‐scale effects are intimately connected with the pressure variations observed in transient saturated flows.