## 5 Conclusions  
In the present study, the efficiency and prediction of four models of high pressure rolling for a WAAM deposited wall, including the 3D short implicit transient model, 3D short explicit transient model, 3D Eulerian steady-state model and 2D short implicit transient model, were evaluated. The computational efficiency and solution accuracy of these models were compared with a conventional large-scale transient model (control model). It was demonstrated that the developed efficient models allowed for the simulation of rolling on the top layer of the built wall, with a computational time of less than one hour, using a desktop computer. This will enable development of efficient models to simulate multi-layer rolling for WAAM components; such simulation is currently unpractical. Based on the results and analyses, following conclusions are made:  
1. The efficiency of a rolling model depends largely on the number of elements (or degrees of freedom) involved in the FEM analysis. Reduction of component length in the model can dramatically improve the computational efficiency without impairing solution accuracy, since steady-state rolling can be established within a region of short length.  
Figure 16: Longitudinal RS distributions: (**a**) prior to rolling; (**b**) after rolling at a load of 10 kN; (**c**) after rolling at a load of 50 kN.  
2. The implicit analysis method is more accurate and efficient than the explicit analysis method for the short rolling models with analytic rigid rollers and relatively low rolling loads.
3. The solution of the 3D short implicit transient model is most accurate among the developed efficient models, as compared to the control model. The accuracy of the 3D short explicit transient model was impaired by the artificially assigned high density of material (mass scaling for acceleration of computation). Reduction of the mass scaling factor improved accuracy, but increased computational cost significantly. The 3D Eulerian steady-state model is less accurate due to unrealistic representation of the rolling process, and its efficiency is limited by the restriction that parallel computation is not supported when the steady-state detection feature is enabled using the employed version of Abaqus software.
4. The 2D implicit transient model cannot capture the 3D deformation mechanism during rolling, and hence it is least accurate in predicting the distributions of longitudinal residual stress and plastic strain. Nevertheless, the 2D transient model is much more efficient than the 3D models, and it could be used for a quick qualitative estimate of the mechanical response of the WAAM component to rolling.
5. Application of an elastic deformable roller instead of an analytic rigid roller in the 2D rolling model barely affected the solution, but significantly reduced computational efficiency.  
Conceptualization, V.G., J.D., Y.S. and S.W.; methodology, V.G.; software, V.G.; investigation, V.G.; writing--original draft preparation, V.G.; writing--review and editing, Y.S. and J.D.; visualization, V.G.; supervision, J.D., Y.S. and S.W.; project administration, J.D. and S.W. All authors have read and agreed to the published version of the manuscript.  
EPSRC grant EP/R027218/1 for the programme of New Wire Additive Manufacturing (NEWAM).  
Not applicable.  
Data Availability Statement: Data underlying this study can be accessed through the Cranfield University repository at [[https://doi.org/10.17862/cranfield.rd.13514419](https://doi.org/10.17862/cranfield.rd.13514419)]([https://doi.org/10.17862/cranfield.rd.13514419](https://doi.org/10.17862/cranfield.rd.13514419)).  
Initial part of this research was guided and supported by [PERSON]. Part of this research was technically supported by [PERSON], [PERSON] and [PERSON]. The support by WAAMMat and NEWAM (EPSRC grant EP/R027218/1) is also gratefully acknowledged.  
The authors declare no conflict of interest.