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Modeling of AM processes is extremely important for the process parameters optimization and to provide prediction of residual stresses and microstructure in the printed parts. Three categories of models can be found in literature: numerical, analytical and empirical. In LPB and LPF processes, melt pool formation, laser particle interaction process, temperature, velocity and thermal stress field distributions over the process, can be simulated by numerical models. Analytical models take into consideration the physics of the processes and the process optimization. In literature, analytical models have been employed to predict the melt pool depth, dilution and the temperature field with given values of clad height and clad width. In their work Fathi and coworkers, used a parabolic equation to build the melt pool’s top surface and the temperature field was predicted solving the heat conduction in substrate based on an infinite moving point heat source. Tan and coworkers, estimated the clad layer geometry based on a moving disc heat source model. An ellipse was used to fit the melt pool and the powder catchment efficiency was calculated directly as the ratio of melt pool and the powder stream area. Most of these models have different prediction accuracy, since they have either decoupled the heat and mass flow interactions in the LPF process or did not take into consideration the changes of the laser power absorptivity. Yuze and coworkers have developed an analytical model that combines the main physical changes of the whole process by coupling the attenuated laser power, the heated powder stream and the semi-infinite substrate with considering their concentration and intensity spatial distribution. The original laser beam intensity distribution on substrate is shown in Figure , with maximum value of 660 J/mm2, while the attenuated laser intensity loss of around 28 J/mm2, by the powder is shown in Figure. The temperature field on substrate surface was obtained coupling the attenuated laser beam and the heated powder stream as the resultant moving heat source, as shown in Figure. Two half ellipses were used to approximate the melt pool projection geometry on the substrate surface, and are displayed as dashed lines in Figure 24c. The modeling and simulation of LPB AM are mostly based on numerical models, which incorporate multi-physics by means of Lattice Boltzmann method or the Lagrangian-Eulerian method and cover either the hydrodynamic or the thermodynamic aspects. Empirical modeling are more time-efficient compared to the numerical models, but are case sensitive, while numerical models requires high computation to capture the complex phenomena in the molten pool. Numerical modeling of LPB AM process consists of simulations at the micro level (melt-pool modeling) and at the macro level (part-level simulation). At the melt-pool modeling level, multiple physics phenomena should be considered: heat conduction, heat convection and radiation, capillary effects, Marangoni effect, photon absorption by particles. Panwisawas and coworkers, taking into consideration most of the interfacial phenomena in their model, they derived the temperature distribution of single-track molten zones. It was demonstrated that the irregularity of the single tracks increased as the laser-scan speed increased. Regarding part level simulations, analytical and numerical modeling has been used to study the residual stresses in the LPB AM processes and to investigate the temperature and stress distributions in one single layer in LPB AM. Analytical models, do not incorporate the multi-physics, and are less common due to the more complex physics behind the LPB AM process. For instance, the model proposed by Knol  describes the process parameters effect on the residual stresses and the porosity through a semi-analytical thermal model. In their model, the authors build the powder bed temperature field adding the analytical temperature solution together with the numerical boundary correction solution. A summary of the input parameters and outputs employed for the modeling of different AM process is presented in the Table.

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