Finite element approach to composite mold design based on Darcy flow with velocity clipping

This article discusses various numerical techniques that are widely used in industry to solve the Darcy flow equations. We outline their merits and limitations. We also present a new stabilized finite element formulation that has been proposed recently (Nakshatrala et al., Comput. Meth. Appl. Mech. Eng., doi: 10.1016/j.cma.2005.07.009). This method is the best available numerical method in the present literature for solving Darcy flow equations and it is the ideal formulation for three-dimensional Darcy flow simulations because of its accuracy and stability characteristics. This formulation can be easily implemented in an existing finite element code and it is the only formulation based on continuous finite elements to pass three-dimensional constant flow patch tests. Next, we present a computational methodology that is based on a velocity clipping finite element approach and a steady-state solution of the Darcy flow equations to model and visualize resin flow during the resin transfer molding process. We show that steady-state Darcy flow can be a valuable tool for a composite manufacturer to decide on the location of the inlets and outlets, and also to visualize resin flow. The methodology is promising for the design of the manufacturing process for complex composite members because it is computationally efficient. We also present a novel approach to model open space within the mold that results from cutting and bending of fibers. In the end, we provide some experimental results and compare them with the numerical results.