## 5 Conclusions  
The SVE-based homogenization approach can be used to derive elastic and fracture properties for SLM materials. The mean apparent values for vertical and horizontal Qols bear a resemblance to the experimentally obtained values. Furthermore, increasing the SVE size reduces the variation in homogenized properties. The relative difference in mean values for \(E_{v}\) was more than twice that for \(E_{h}\), indicating heightened sensitivity in the effect of SVE size on vertical stiffness. The behavior in the horizontal and vertical directions appears to exhibit inverse tendencies, with the vertical direction displaying heightened sensitivity in linear components while the horizontal direction demonstrates increased variability during fracture, indicating divergent behavior between the two directions. The difference in behavior between horizontal and vertical results can be attributed to the microstructure of the SLM material. The likelihood of a melt pool boundary perpendicular to the applied load is greater for the vertical load case than for the horizontal load case. The resulting over-stiffness phenomenon observed for the horizontal load case decreased for larger SVEs. As for fracture properties, we observe that they exhibit higher variations and less stable mean values when compared to those of elastic properties. In any case, for the SLM material considered, below or around the size of 140 \(\upmu\)m, all elastic and fracture properties reached both the mean- and variation-based RVE size. The results provide insights into how SLM materials' elastic and fracture properties tend toward their macroscopic size-independent and homogeneous limit. While these RVE-based limits are suitable for many macroscopic problems, SVE-based homogenized properties are favorable for failure analysis as they maintain a sufficient level of material heterogeneity needed for such applications [26, 41]. The heightened sensitivity of fracture properties to small variations in SLM materials bears significant implications for material design and structural integrity. A more comprehensive understanding of the brittleness and fracture behavior becomes critical since even minor variations in these properties can potentially lead to catastrophic brittle failures in real-world applications. We believe that these SVE-based elastic and fracture properties can be used for the stochastic failure analysis of materials as demonstrated in [30]. Some other extensions of this work are as follows. First, we only had one set of experimental results to compare with our computational results. To accurately validate the results, we should have several experimental strain-stress responses of the SLM material for each SVE size considered. Second, the temperature effects during manufacturing and ensuing residual stresses should be included in subsequent mechanical analysis. These residual stresses are obtained from the thermomechanical analysis of the printing process [49]. Some examples of such analysis for a single laser path, multiple parallel paths, and an entire SLM part are provided in [50, 51], and [52], respectively. In future work, we aim to derive residual stresses resulting from simulating the manufacturing process and incorporating their effect on the nonlinear properties of the printed material, such as strength and fracture energy. Third, grain-level nonlinear material models such as crystal plasticity remove the restriction of crack propagation along melt pool boundaries and provide a more accurate overall representation of material failure. Fourth, SVE-based homogenization can be incorporated in the multiscale linear and nonlinear analysis of SVEs. The lower computational cost of such multiscale analyses (compared to that for DNS) makes this approach a suitable forward solver in design problems, for example in optimizing SLM printing parameters [50, 53]. Conceptualization, R.A., S.S., C.T.F. and K.L. ; methodology, R.A. and S.S.; software, B.V., R.P.C., G.H., and R.A.; validation, R.P.C. ; formal analysis, R.P.C. ; investigation, R.P.C.