## 4 Results and Discussion
### Cyclic Plasticity Simulation  
The parameters of the kinematic hardening rule (Equation (1)), used in both the isotropic and anisotropic plasticity model, were calibrated manually (employing a successive trial and error continuous optimisation approach) from the experimental hysteresis loop data (for the vertical coupon). These parameters are listed in Table 2. Moreover, the yield stress was calibrated to \(\sigma_{y}\) = 420 MPa to account for the cyclic properties of the material (as opposed to using the yield stress measured from monotonic tensile tests).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Kinematic Hardening**} \\ \hline \(c_{1}\) & 241,800 & \(\gamma_{1}\) & 930 \\ \(c_{2}\) & 98,280 MPa & \(\gamma_{2}\) & 945 \\ \(c_{3}\) & 14,112 MPa & \(\gamma_{3}\) & 96 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the kinematic hardening rule for the as-built EOS MS300, used in both the isotropic and the anisotropic plasticity model.  
Figure 2: The hysteresis loops of the tested as-built EOS MS300 horizontal and vertical test coupons (at the 28 th cycle) and the [PERSON] et al. [10] published data for the as-built MS300 vertical coupon.  
For the isotropic hardening model, the Elasticity Modulus, \(E\), selected was 160 GPa and the Poisson ratio, \(\
u\), was 0.35 (based on the data reported in [5]).  
The coefficients of the Hill anisotropic yield surface (Equation (2)) and the orthotropic Hooke's law (Equation (3)) (anisotropic plasticity model) were obtained from a previously published paper [11] on the same material (as-built EOS MS300). These coefficients are listed in Table 3. The methodology for the calculation of these coefficients is outside the scope of this paper; therefore, the reader is referred to the same publication for a detailed description [11].  
The two plasticity models were implemented for this study's experimental data (hysteresis loops stress-strain curves), derived from the two tested coupons (horizontal, vertical). Figure 3 presents the simulation results, where a good prediction of the experimental data can be observed. Of particular interest is that a closer prediction was obtained with the anisotropic plasticity model, which is attributed to the more representative description of the (elastic and plastic) anisotropy of the as-built EOS MS300 (measured in [5]). This is more clearly evidenced in the case of the horizontal test coupon data, where the hysteresis loop is simulated very well.  
This, qualitative comparison is complemented by a calculation of the average error between experimental and simulated data (across the range of the stress-strain curve). The results of this calculation are included in Table 4, where the clear advantage of adopting the anisotropic plasticity model over the isotropic model is confirmed again.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Isotropic** & **Anisotropic** \\ \hline
**Vertical** & 43.5\% & 36.3\% \\
**Horizontal** & 58.6\% & 21.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average error (%) for the vertical and horizontal test coupon experimental and simulation data for the isotropic and the anisotropic plasticity model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Hill** & \multicolumn{4}{c}{**Orthotropic Hooke**} \\ \hline F & 0.798 & **E1** & 137 GPa & \(\
u_{12}\) & 0.43 \\
**G** & 0.638 & **E2** & 161 GPa & \(\
u_{21}\) & 0.93 \\
**H** & 0.202 & **E3** & 122 GPa & \(\
u_{13}\) & 0.26 \\
**L** & 1.167 & **G12** & 122 GPa & \(\
u_{31}\) & 0.01 \\
**M** & 1.500 & **G12** & 122 GPa & \(\
u_{23}\) & 0.24 \\
**N** & 1.500 & **G23** & 122 GPa & \(\
u_{32}\) & 0.35 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficients of the Hill anisotropic yield surface and the orthotropic Hooke’s law tensor for the as-built EOS MS300, used in the anisotropic plasticity model [12].