## 2 Materials and Methods
### Methodology of Numerical Simulation  
#### 2.2.1 Boundary Conditions, Build Geometry and Material Properties  
Figure 6 represents the solution domain for thermal and mechanical simulation. The domain was created using a mesh and geometry generation toolkit CUBIT by Sandia National Laboratory. The characteristic mesh size used in the simulation was 1.6 mm for the Ti-wall and the Ti-plate, corresponding to the bead height. An approximately three times coarser mesh of 4.8 mm was used for the steel plate, for computational efficiency. The numerical solution was calculated using the commercial finite element method (FEM) package, ABAQUS 2018 [16]. The detailed features of the ABAQUS AM module and simulation have been addressed in earlier literature [4, 5, 17]. The model has 189,028 3D 8-node linear isoparametric hexahedral elements for heat transfer (DC3D8) and stress (C3D8) analyses. The model domain consists of Ti-wall, Ti-plate, and steel plate. The dimensions of the Ti plate were 300 mm (L) \(\times\) 210 mm (W) \(\times\) 6.35 mm (H), and the Ti-wall was 175 mm (L) \(\times\) 19.2 mm (W) \(\times\) 75 mm (H).  
In the experiment, four and fourteen clamps were applied for the center clamp and full clamp conditions, respectively, to hold the Ti plate to the base plate. Ideally, the Ti build plate should be in full contact with the base plate. However, the two contacting surfaces of the solid plates are not perfectly smooth, so, practically speaking, there is a variable gap present along the interface. As the heat is  
Figure 5: Plate Faro-scan for the build with double beads.  
Figure 6: Computation solution domain for thermal and mechanical simulation.  
transferred from the hot build plate to the colder base plate, a noticeable temperature drop can be found at the contact interface. This physical phenomenon is called thermal conductance [18]. There are several factors influencing the thermal conductance, such as asperity between two interstate contacts, contact pressure, cleanness, and plate deformation. The gap distance between two contacts can vary with the plate deformation caused by thermal expansion or shrinkage during printing. Since it is hard to precisely determine the variation of thermal conductance at all locations throughout the experiment, the simulation considers the thermal contact as a model parameter. The thermal contact between the Ti build plate and base plate is modeled as a surface tie. The heat transfer values of 1.4 mW/mm\({}^{2.\circ}\)C, 1.0 mW/mm\({}^{2.\circ}\)C and 0.85 mW/mm\({}^{2.\circ}\)C were applied to three sectioned areas on the base plate based on clamp locations.  
A moving laser heat source is described as a point-concentrated heat source due to the relatively large element size compared to the melt pool. The heat source acts in the cuboidal element and moves according to the tool path. A combined heat transfer coefficient of convection and radiation was calibrated and used for heat loss through the surrounding environment [19]. The original equation is expressed below  
\[h_{comb}=\varepsilon\cdot 24.1\times 10^{-4}\cdot T^{1.61} \tag{1}\]  
where \(h_{comb}\) is the combined heat transfer coefficient and \(\varepsilon\) is emissivity.  
Homogeneous and temperature-dependent thermo-mechanical properties are used in the simulation. The isotropic plasticity model was used to consider the mechanical response. The properties were obtained from material simulation JMatPro and literature [15; 20; 21]. The values used in the simulation are listed in Appendix A Tables A1 and A2.