## 4 Application to an Additive Manufacturing Benchmark Test  
To model the SLM process, we used Ansys additive software [43] that employs a thermo-mechanical coupling method to simulate the SLM process, as shown in Figure 5. The heat transfer analysis provides the transient temperature field that is transferred to the mechanical analysis model [43]. The same workbench additive model has been used in many similar studies [44; 45; 46] to validate the code and to optimize the SLM build part. To set up an AM simulation in Ansys, we can either create our geometry in the software or we can import the stl. format of the geometry. In addition, the software gives the freedom to create supports during the simulation, or it can generate them automatically depending upon the given conditions. However, in this study we did not consider any support structure. After the geometry setup, the whole domain was divided into several layers depending on the layer thickness. To simulate each layer, we used the cartesian coordinate mesh with an element birth method to activate the elements in each building step. The numerical model sets the elements in the whole layer to the melting temperature at once, assuming that the developed temperature is always at or above the melting temperature but it does not significantly exceed it. During the melting of the powder, the scan pattern is not considered as an input parameter. Additionally, the unmelted surrounding powder is not explicitly modeled, instead the heat loss between the powder and the solid material boundary is simplified using the convection boundary condition at the interface. A convection boundary condition was used for each heating and cooling  
Figure 4: Differential Evolution. Figure 5: Flow chart of Ansys additive simulation. step, but the radiation boundary condition is not considered in the model. The powder and the gas convection coefficients were 1.8 \(\times\) 10\({}^{-5}\) W/mm\({}^{2. }\)\({}^{\circ}\)C and 2.4 \(\times\) 10\({}^{-8}\) W/mm\({}^{2. }\)\({}^{\circ}\)C respectively. The pre-heat powder temperature was set at 80 \({}^{\circ}\)C whereas, the chamber and the base plate temperature were maintained at 40 \({}^{\circ}\)C and 80 \({}^{\circ}\)C respectively. The other process parameters related to the machine and the material are described in the following subsections. Further details can be found in [47, 48]. To validate the numerical results presented in this work, we compared the strains and the part deflection results with the experimental data of a benchmark case, AMB2018-1, provided by the National Institute of Standards and Technology (NIST) [48]. In 2018, the NIST provided a set of experimental results for different additive manufacturing processes, including SLM. All the details about the experimental setup and the operations for AMB2018-1 are available on the NIST website [9]. This benchmark study aimed to provide reliable stress, strain, and deflection benchmark data in a bridge-like structure. A brief description of this benchmark case, shown in Figure 6a,b, is provided here. The residual stress and strain data were measured using x-ray diffraction and neutron diffraction methods. For the part deflection measurement, the bridge was partially separated from the base plate, and then a coordinate measurement machine was used to measure the deflection. The AM part was constructed using two different machines: the NIST in-house-built machine AMMT (additive manufacturing metrology testbed) and the EOS M270. In the present study, we considered only the EOS M270 machine, as the measurement results for the part deflection were not available for the structure constructed with the AMMT. More details on the process can be found in [48]. The test case comprised four bridge structures on a build plate, as shown in Figure 6b. All four bridges and the substrate were constructed using IN625 material with a powder bed fusion process. During the process, the bridges were built with some spacing (Figure 6b).