## 3 Results
### Effect of Spatial Uncertainty on the Mechanical Behavior of Additively Manufactured Struts
Table 3 shows the maximum von Mises stresses of the volume-matched geometry strut and the predicted AM strut normalized with respect to the maximum von Mises stress of the nominal strut. The von Mises stress distribution and the location of the maximum value is displayed in Figure 7d. The stress distribution in Figure 7d shows distinctive difference from the stress distribution in the vertical strut because of two major factors: (1) bending and shear stresses and (2) surface roughness. When a strut is loaded axially, it only develops compressive normal stress. When a strut is loaded with an angle, bending and shear stresses begin to arise, and it becomes more likely that the strut undergoes a large deformation and becomes more susceptible to developing a large stress as shown in Figure 7d. In addition to the effect from bending and shear stresses, local stress concentrations are observed near the side profiles in the predicted AM, which is not observed in the volume-matched strut or the nominal strut in which the sidewall profiles are smooth. The geometric discontinuities caused by the spatial uncertainties change the stress distribution in the strut, and the amount of stress concentration is thrice that in the smooth cases. Thus, it is anticipated that the total stiffness of the additively manufactured strut is affected by the change in stress distribution. Therefore, considering spatial uncertainties in the geometry to accurately predict the mechanical behavior of struts using FE analysis is essential. Figure 7: Compression test results of additively manufactured struts: (**a**) Loading and boundary conditions of three struts: nominal, predicted AM, and volume matched struts; (**b**) Stress–strain curve of nominal, predicted AM, and volume-matched struts in different printing angles (90\({}^{\circ}\), 75\({}^{\circ}\), and 60\({}^{\circ}\)); (**c**) Normalized effective stiffness of volume-matched geometry and predicted AM struts in different printing angles (90\({}^{\circ}\), 75\({}^{\circ}\), and 60\({}^{\circ}\)); (**d**) Normalized von Mises stress distributions in a predicted AM strut and a volume-matched strut. The proposed modeling framework is also applicable to complex AM parts with inner structures. The spatial uncertainties can be estimated by the proposed modeling framework if the inner structure of the complex AM parts is expected to exhibit spatial uncertainties that are statistically similar to the outer structure. Even if the inner structures of the complex AM parts are expected to exhibit statistically different spatial uncertainties, the proposed modeling framework can be still applied to the complex AM parts with the exception of the image segmentation sub-step. As opposed to the use of optical images, there are multiple techniques to measure the inner structure profile of the complex parts, such as X-ray computed tomography and profilometry. Following the extraction of the inner structure profile, it is possible to apply the remaining sub-steps of the proposed modeling framework, namely variability-based sampling and Gaussian process modeling, to the problem.