## 4 Discussion
### Steady-State Rolling and Its Implicaiton in Computational Efficiency  
The steady-state rolling is of major interest for analysis since it dominates the mechanical response of the WAAM component to the rolling. The efficient model is effective and acceptable if it can capture the steady-state rolling. It was demonstrated that all the efficient models developed here had sufficient wall length to obtain a stable and consistent solution for the steady-state rolling (Figure 5). The computational efficiency of the 3D short explicit transient model could be increased further by reducing the wall length in the model, since the whole length was still considerably larger than the length of the region where steady-state rolling was established (Figure  
accuracy of the model solution, as long as the steady state was reached. Moreover, the same mesh topology and Abaqus Standard solver (implicit method) were used in both models. The slight discrepancy in the results could be attributed to the applied constraints on the Start and End boundaries in the short model, which could lead to enhanced stiffness in the rolling direction. The solution accuracy of the short explicit transient model (Figures 8 and 9) was impaired by the artificially increased density of the material, as a result of the mass scaling which was used to accelerate computation. The increased density could exacerbate the effect of inertial force which could violate the equilibrium state assumed in the rolling process. As found in a parametric study conducted in this research, using lower values of mass scaling factor made the short transient explicit model more accurate, but led to significantly lower efficiency compared to the short implicit transient model. This confirmed the findings of [PERSON] et al. [54] and [PERSON] et al. [55] that the implicit solver is more accurate and less computationally expensive than the explicit solver for relatively simple contact problems with rigid bodies involved. Nevertheless, an explicit analysis still has the potential to better handle complex contact problems and large deformations than an implicit analysis. Furthermore, the short explicit transient model reached steady state earlier than the short implicit transient model (Figure 5). This allowed further reduction of the wall length, and as a result, a considerable reduction of elements used in the analysis could be achieved. From a numerical algorithm point of view, the explicit solution method was better suited to parallel computation than the implicit method. The Eulerian model was less accurate than the short implicit and explicit models due to the unrealistic rolling process simulated in the Eulerian model. The control model simulated the actual rolling process in reality [3], in which the deformable wall remained steady and the roller moved along the wall, causing the free rotation of the roller due to friction between the roller and the wall. In contrast, in the Eulerian model, the torque was applied to the steady roller, and the wall material movement was caused by the rotation of the roller and the friction between the roller and the wall. The friction caused material to \"stick\" to the roller, and the applied torque drew the material underneath, which increased longitudinal tensile PS under the roller (3 mm below the rolled surface) as compared to the control model (Figure 9). As a result, larger tensile deformation and higher compressive longitudinal RS were generated in this region (Figure 8). More extensive stretching of material due to the applied torque occurred as well on the rolled surface, which caused longitudinal tensile RS (Figure 8). As the Eulerian model also employed an explicit solver, similar issues to the short explicit transient model could affect the solution accuracy of the Eulerian model. The 2D plane stress model did not accurately represent a rolling process for the WAAM component in which the RS and PS were non-uniformly distributed in the through-thickness direction of the wall (Figures 13 and 14).