On the Alternate Direction Implicit (ADI) Method for Solving Heat Transfer in Composite Stamping

Thermostamping of thermoplastic matrix composites is a process where a preheated blank is rapidly shaped in a cold matching mould. Predictive modelling of the main physical phenomena occurring in this process requires an accurate prediction of the temperature field. In this paper, a numerical method is proposed to simulate this heat transfer. The initial three-dimensional heat equation is handled using an additive decomposition, a thin shell assumption, and an operator splitting strategy. An adapted resolution algorithm is then presented. It results in an alternate direction implicit decomposition: the problem is solved successively as a 2D surface problem and several onedimensional through thickness problems. The strategy was fully validated versus a 3D calculation on a simple test case and the proposed strategy is shown to enable a tremendous calculation speed up. The limits of applicability of this method are investigated with two parametric studies, one on the thickness to width ratio and the other one on the effect of curvature. These conditions are usually fulfilled in industrial cases. Finally, even though the method was developed under linear assumption (constant material properties), the strategy validity is extended to multiply, temperature dependant (nonlinear) case using an industrial test case. Because of the standard methods involved, the proposed ADI method can readily be implemented in existing software.