Barone-Caulk model

In your university library, find the paper Barone, M.R. and T.A. Osswald, J. of Non-Newt. FluidMech., 26,185-206, (1987), and write a 2D FEM program to simulate the compression molding process using the Barone-Caulk model presented in the paper. Compare your results to the BEM results presented in the paper. 

The solution to the full set of conservation equations for mass, momentum and energy requires major computational resources and may become very costly. Instead, some assumptions are introduced to obtain simplified flow models. The most popular models are the generalized Hele-Shaw (GHS) model and the Barone-Caulk model. 

The GHS model is simple and computationally efficient because the formulation consists of only one governing equation in terms of one variable, namely, pressure. Whereas the GHS model applies to thin cavities, the Barone-Caulk model better predicts the flow of thick charge (Erwin and Thcker, 1995 Lee, 1984). The Barone-Caulk model characterizes the flow by uniform extension though the cavity thickness with a slip boundary condition between the charge surface layers and the mold surfaces instead of the no-slip condition that is adopted in the GHS model (Barone and Caulk, 1985,1986). For further information on the Barone-Caulk model, the readers are recommended to see the references providing comprehensive description and simulation examples (Davis et al, 2003 Tucker, 1987). 

Recently, Dumont et aL improved the Barone-Caulk model considering the non-Newtonian behavior of SMC (Dumont et al, 2007). Assuming SMC to be an incompressible and purely viscous material, they proposed a transversely isotropic rheology model. The basic governing equations for the SMC flow are the mass conservation and the momentum balance equations. 

Both models can be solved by different numerical schemes. The boundary element method has the advantage that the velocity gradient can be obtained more accurately than the finite-element method, which is important for predicting the fiber orientation (Barone and Caulk, 1986 Osswald and Thcker, 1988). However, it is restricted to single charge, flat parts and cases of uniform thickness. Hence, many simulation efforts have converged to the use of the finite-element/control-volume method (Erwin and Thcker, 1995 Osswald and Tucker, 1990) coupled with the volume of fluid (VOF) method to track the position of flow front (Hirt and Nichols, 1981). 

Barone, M. R. and Caulk, D. A. (1986), A model for the flow of a chopped fiber reinforced polymer compound in compression molding . Journal of Applied Mechanics, 53(2), 361-371. 

Barone MR, Caulk DA. A model for the flow of a chopped fiber reinforced polymer compound... 

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