## 3 Results
### Solution Accuracy  
The accuracy of the efficient models was examined through comparison with the large scale implicit transient model, which was based on the actual dimensions and rolling process of the WAAM component built in the previous experiment [35] and hence used here as the control model. Figure 8 presents longitudinal RS distributions on the inspection planes for different rolling models. All models predicted tensile RS with a magnitude up to 582 MPa underneath the rolled surface and compressive RS with a magnitude up to 545 MPa underneath the tension zone. The peak of the compressive RS shifted towards the outer surface of the wall (opposite to the symmetry plane). The short implicit transient model predicted the most accurate RS distribution compared to the control model. The short explicit transient model and the Eulerian steady-state model predicted larger regions under tensile RS, and the Eulerian model predicted larger magnitudes of both tensile and compressive RS. Figure 6: Reaction forces obtained at the rotation point of the rollers (note that only half of the WAAM component was considered in the models). Figure 7: Contact pressure during rolling in 3D short implicit transient model. Figure 9 shows the longitudinal PS distributions on the inspection planes for different rolling models. All models, except the Eulerian model, predicted concentrated tensile PS immediately under the rolled surface, while the Eulerian model predicted the highest tensile PS further underneath the rolled surface, which was concentrated on the side surface of the wall. The models predicted compressive PS in regions relatively far from the rolled surface. The longitudinal PS distribution predicted by the short implicit transient model was in best agreement with that predicted by the control model. Figure 10 shows the normal PS distributions on the inspection planes for different rolling models. Compressive PS was dominant in the deformed region, and the peak PS  
Figure 8: Longitudinal residual stress (RS) distribution on the inspection plane: (**a**) large scale implicit transient model (control model); (**b**) short implicit transient model; (**c**) short explicit transient model; (**d**) Eulerian steady-state model. Figure 9: Longitudinal plastic strain (PS) distribution on the inspection plane: (**a**) large scale implicit transient model (control model); (**b**) short implicit transient model; (**c**) short explicit transient model; (**d**) Eulerian steady-state model. was located approximately 2.2 mm below the rolled surface and close to the symmetry plane. No considerable tensile PS was found in the wall. The predictions of normal PS by all the efficient models achieved similar agreement with that obtained by the control model. Figure 11 compares the transverse PS distributions predicted by different models. The predicted results were similar between all the models. In contrast to the normal PS, the transverse PS was overwhelmingly tensile. The peak PS was located in the central portion of the deformed region. Figure 12 compares the transverse displacement distributions predicted by different rolling models. There was an overall similarity between the results, while the displacement contour obtained by the Eulerian model was somewhat elongated in the vertical direction. Figure 11: Transverse PS distribution on the inspection plane: (**a**) large scale implicit transient model (control model); (**b**) short implicit transient model; (**c**) short explicit transient model; (**d**) Eulerian steady-state model. Figure 10: Normal PS distribution on the inspection plane: (**a**) large scale implicit transient model (control model); (**b**) short implicit transient model; (**c**) short explicit transient model; (**d**) Eulerian steady-state model. 2D vs. 3D Rolling Models  
Figures 13 and 14 compare the longitudinal PS and RS distributions, respectively, as obtained from the 3D large scale model (control model) and the 2D short transient models with elastic roller and analytic rigid roller.