## 3 Results
### Horizontal Direction  
Figure 12 shows strain versus stress results in the horizontal direction for SVEs of sizes \(L_{SVE}=56\) and \(L_{SVE}=140\)\(\upmu\)m, respectively. Compared to the corresponding results for vertical loading in Figure 10, there is less variation in the elastic modulus and delayed softening past the maximum stress for the horizontal loading results. We contribute these features to the topology of the melt pools in Figure 2a. The melt pool boundaries are more favorably opened when the loading is along the vertical direction compared to when it is in the horizontal direction. This is due to the fact that for horizontal loading, there are long stretches of material from left to right that carry the load and contain no melt pool lines. Accordingly, separation along the cohesive surfaces is not activated as much. The results show less variation and unloading past the maximum stress given that the response is mostly driven by the elastoplasticity of the bulk material.  
Figure 13 shows the PDF and size effect results for the horizontal stiffness. Referring to Figure 13b, stiffness for the horizontal load case is not as heavily affected by the varying SVE size as the vertical stiffness is in Figure 11b. Otherwise, both the vertical and horizontal stiffnesses show the same trends in the PDFs and size effects. That is, in both cases, the mean value stays relatively insensitive to the SVE size. The mean value for each SVE size also closely aligns with the publish value for \(E_{h}\) in Table 1. This is reflected by the red dot corresponding to the experimental results in [38] for the RVE in Figure 2a.  
Figure 11: Vertical results for \(\sigma_{v,\text{max}}\): (**a**) PDF of \(\sigma_{v,\text{max}}\) for all SVE sizes. The red dot serves as a reference to the published value from [38]; (**b**) the size effect plot for \(\sigma_{v,\text{max}}\).  
Figure 12: Horizontal stress vs. strain overlay for (**a**) \(L_{SVE}=56\)\(\upmu\)m; (**b**) \(L_{SVE}=140\)\(\upmu\)m.  
Figure 14 shows the results for horizontal strength \(\sigma_{h,max}\). Referring to the PDFs in Figure 14a, the mean value for \(\sigma_{h,\text{max}}\) varies more dramatically, close to tenfold more, compared to the elastic modulus \(E_{h}\). Again, the red dot corresponding to the experimental results in [38] is provided for comparison with computational results of different SVE sizes. Figure 14b illustrates the increase in both the mean and minimum homogenized value of \(\sigma_{h,\text{max}}\) as SVE size increased. The reason for the increase to \(\sigma_{h,\text{max}}\) at larger SVE sizes and the difference between horizontal and vertical elastic moduli is explained by referring to the geometry of the melt pools in Figures 2a and 5. For large SVEs, there is a higher likelihood of having a whole block of bulk material that runs across the entire SVE. Such blocks prevent the failure of the SVE through debonding across cohesive surfaces, as none will run across the layer. These stiff layers dictate the overall stiffness in the horizontal direction; the 3D printed layers in this case act as parallel springs, wherein the highest stiffness (the continuous layers) dictates the overall stiffness. For small SVEs, there is more likelihood of having certain melt pool lines cut through a layer. Accordingly, the overall horizontal strength becomes lower for such small SVEs. In contrast, for all SVE sizes, the debonding in the vertical direction is easier and almost always possible, thus much less size sensitivity is observed in Figure 11 for \(\sigma_{v,max}\). The decrease of variations for \(E_{h}\) and \(\sigma_{h,\text{max}}\) is expected as both properties tend to their variation-based RVE size as the SVE size increases [12].