Keywords: post-processing techniques, Darcy flow, Stoke flow, free boundary flows, mesolevel analysis, capillary pressure, liquid composite molding.

New trends in the transportation industry require the implementation of fiber reinforced composites, because of their design versatility, low weight, high mechanical performance tailorable to the industrial requirements, resistance to the environmental conditions, net shape and sometimes possibility of an easy repair and/or recycling. Structural pieces fabricated by pre-preg technology are being replaced by components manufactured by recent methodologies called liquid composite moulding processes (LCM). Among them, resin transfer moulding (RTM), vacuum assisted resin transfer moulding (VARTM) and vacuum assisted resin infusion (VARI), belong to the group of low injection pressure processing techniques. When large products in smaller series are required, demands on further cost reduction, which can be achieved either by cycle time decrease or moulds manufacturing cost reduction, are becoming crucial. Then VARTM and VARI, happen to be more attractive, as they require only one rigid mould face and can be processed under room temperature. Physics of the resin advance and thickness variation in these technologies is not yet fully understood and therefore the risk of failure during production of large pieces is still considered too high.

Reliable flow simulation software is essential in determination of an optimal injection strategy. Available simulation software is usually based on Darcy's law, suited for macrolevel analysis and capillary action is either omitted or not accounted for correctly. Void formation during the injection phase can be explained as a consequence of the non-uniformity of the flow front progression. he origin of this fact lies in the dual porosity of the fiber preform and therefore the best explanation can be provided by mesolevel analysis. In the mesolevel analysis, liquid flowing along two different scales must be considered. Single scale porous media (fiber tows) and open spaces are presented and therefore different flow regimes are linked together. In this simulation it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. Correct implementation of the capillary action allows extension of simulations to the vacuum assisted processes, where wicking flows dictate the resin advance [1].

Numerical techniques to address the movement of the flow were already developed in the free boundary program (FBP) [2]. Numerical simulations can track the advancement of the resin front promoted by both hydrodynamic pressure gradient and capillary action. Base analysis is solved in commercial code ANSYS. However, capillary action implementation brings numerical difficulties, when continuous Galerkin method is used. This can be overcome by post-processing of the free-front normal velocities yielding superior convergence results. "Post-processing" a finite element solution is a well-known technique [3], which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. These techniques are especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. The recalculation exploits the previous finite element solution and makes use of the space of trial shape functions that were omitted in the original formulation [4]. Consequently such an approach can be exceptionally good in modeling of resin infiltration under quasi steady-state assumption by re-meshing techniques and with explicit time integration, because only the free-front normal velocities are necessary to advance the resin front to the next position. The new contribution is the "post-processing" of the free-front velocities of mesolevel infiltration analysis, which allows achieving better accuracy on even coarser meshes, and which in consequence reduces the computational time also by the possibility of implementing larger time steps. Recalculation is simple and fast and especially for triangular elements does not bring any complications. Currently is it performed by software Maple procedure directly implemented in FBP. Benefits of this technique are demonstrated on several examples. Numerical simulations are focusing on reproducing of the void formation physics.

1

S.G. Advani, Z. Dimitrovová, "Role of Capillary Driven Flow in Composite Manufacturing", in Surface and Interfacial Tension: Measurement, Theory and Applications, ed. S. Hartland, Surfactant Science Series, 119, 263-312, 2004, Marcel Dekker, Inc., NY.

2

Z. Dimitrovová, S.G. Advani, "Mesolevel analysis of the transition region formation and evolution during the liquid composite molding process", Computers & Structures, 82, 1333-1347, 2004. doi:10.1016/j.compstruc.2004.03.029

3

I. Babuška, A. Miller, "The post-processing approach in the finite element method - Part 1: Calculation of displacements, stresses and other higher derivatives of the displacements", International Journal for numerical methods in Engineering, 20, 1085-1109, 1984. doi:10.1002/nme.1620200610

4

T.J.R. Hughes, G. Engel, L. Mazzei, M.G. Larson, "The continuous Galerkin method is locally conservative", Journal of computational Physics, 163, 467-488, 2000. doi:10.1006/jcph.2000.6577

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