Framework Of Mixture Theory Research Articles

Abstract This study accounts for the necessity of developing a proper mathematical model of composite material processes in order to implement it in a numerical simulation. The process considered here is the resin transfer moulding (RTM). It essentially consists of the injection of a polymeric resin in a porous pre-form of reinforcing elements. Process simulation is of considerable value in assessing production parameters and in improving the quality of manufactured products. The proposed model is deduced in the framework of mixture theory. In particular, a solid–liquid–air mixture is considered. The porous solid is deformable and its mechanical behavior is non-linear elastic. The model consists of a set of partial differential equations, time dependent, defining two coupled problems: mechanical equilibrium and diffusion in a permeable medium. The equations are written, at first, in the Eulerian formulation and then, considering a set of material coordinates fixed on the porous solid, in the Lagrangian formulation. The mathematical problem, generated by the model, is defined in the whole domain occupied by the mixture of three-phases. It is shown that, if the transitional layer between the region wet by the infiltrating liquid and the one not reached by the liquid is thin, then the formulation proposed is equivalent to the classical formulation where different sets of equations are used for different regions. The problem is solved numerically by means of finite element method. The simulations developed use the ABAQUS FEA package. Two 3D infiltration problems are simulated. Although the simulations do not refer to any practical applications, the results show the usefulness of the model in the assessment of process parameters in true industrial problems.

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