Optimization of composite forming processes using nonlinear thermal models and the proper generalized decomposition

Abstract

The potential of reduced order models to improve computational efficiency without any loss of behavioral fidelity, is attracting many researchers. Indeed, the reduced order models appear to be efficient for linear models. However, the challenge isn't won yet facing the nonlinear models. The Proper Generalized Decomposition (PGD) is one of the popular reduced order models techniques. In fact, it reduces the computation time by separating the space dimensions and therefore reducing the dimensionality of the problem. Moreover, the PGD treats nonlinearity by a linearization step, using iterations for example. However, the aim of using reduced order models is the computation time reduction. Using iterative linearization techniques, computation time reduction becomes irrelevant and therefore new techniques should be proposed. In this work we propose a new linearization method by combining the PGD and the POD (Proper Orthogonal Decomposition). The treated problem rises from thermoset materials' curing where a coupling between the nonlinear heat equation and the nonlinear curing kinetics exists.