SIM-AM 2023

Macroscopic thermomechanical modeling of DED additive manufacturing: coupling Inherent strain rate method and POD-Galerkin-based model reduction

  • KEUMO TEMATIO, Joel (MINES Paris, UMR CNRS 7635)
  • BELLET, Michel (MINES Paris, UMR CNRS 7635)
  • RYCKELYNCK, David (MINES Paris, CNRS UMR 7633)
  • ZHANG, Yancheng (MINES Paris, UMR CNRS 7635)

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The Directed Energy Deposition (DED) processes are additive manufacturing processes in which focused thermal energy is used to fuse materials by melting as they are being deposited. To optimize the process parameters in terms of distortion and stress prediction, numerical thermo-mechanical modeling is a good approach, as it allows minimizing expensive and time-consuming experiments. However, the non-linear thermomechanical calculation is costly. In this work, we focus on the complexity reduction of the macroscopic thermomechanical modeling of DED processes under the frame of finite element method. As the plastic strain rate is mainly localized within a small region near the deposition, this makes possible a linearization of the initial elastic-viscoplastic mechanical resolution. In practice, a prediction-correction algorithm is developed. The predictor step consists of the linearized mechanical resolution, in which the generalized plastic strain rate is deduced from the previous resolutions. This is why the method is named "inherent strain rate". The corrector step consists in a local (e.g., in each finite element) reconstruction of the effective stress field by solving a local non-linear scalar equation. This predictor/corrector strategy is employed to deal with the dynamic evolution of strain rates and stress, in which the two situations of deposition on one hand and dwell time on another hand are treated in a different way. With the above method, a time gain of 5 is obtained, while the results (distortion and stress) of the full non-linear thermomechanical resolution are replicated with an excellent accuracy. To further reduce the computational cost, POD-Galerkin-based model reduction is proposed to couple the Inherent strain rate method. The main purpose of this step is to reduce the number of degrees of freedom of the equilibrium equation to be resolved. Finally, a time gain of around 30 is achieved by maintaining the prediction quality for both distortion and stress. The two-step complexity reduction method, by coupling the Inherent strain rate and POD-Galerkin-based model reduction, provides an efficient solution for parametric analysis for DED processes.