## 2 Materials and Methods
To apply the MBC for the tensile loading in the horizontal direction, the top and bottom sides of the SVE are modeled as rollers (zero tangential traction and normal direction), whereas the left and right sides are gradually taken apart by applying opposing spatially uniform and temporally increasing displacement values across all nodes. The terminal value of the applied displacement of SVEs in the horizontal direction is chosen to be large enough so that most SVEs undergo failure through the loading process. For the tangential direction, zero traction is specified for these sides too. We refer the reviewer to [26] for a more thorough description of the MBC and its comparison with the KUBC and SUBC. The average strains and stresses of the SVEs were computed using a Python script. With the average stresses and strains of the three load cases, the elasticity stiffness was computed using the process described in [26]. The compliance matrix was computed as the inverse of the stiffness matrix. Finally, the vertical and horizontal elastic moduli, denoted by \(E_{v}\) and \(E_{h}\), were computed from the compliance matrix. To establish an effective failure model for each SVE, one must consider the interaction between each melt pool, i.e., the boundary between melt pools in Figure 5(a) (corresponding to melt pools in Figure 2a). Since the fusion zone is melted and deposited on top of the heat-affected zone, there must exist an interface between the two [3]. Several works including [5; 9; 10] treat such melt pool boundaries as weak interfaces, whose failure response is represented by a cohesive traction-separation relation (TSR). Figure 6 shows the bilinear TSR used for this study. This TSR is characterized by the initial tangent modulus, \(k\), strength value, \(\sigma_{\text{max}}\), and the work of separation (fracture energy), \(\phi\), which is the area under the traction-separation relation. Figure 6: Bilinear traction separation relation (TSR) modified from [42]. Table 1 shows experimentally measured vertical and horizontal elastic moduli and strengths for the sample shown in Figure 2a from [38]. Our objective is to calibrate the elastic and fracture properties of SLM at the melt pool scale, e.g., bulk properties and melt pool boundary TSR parameters, so that the computationally homogenized elastic and fracture properties for the RVE match the results shown in this table. The last two columns of the table show our computational results for a domain that is half the size of the domain shown in Figure 5a in each direction. As evident, there is a good match between experimental and computational elastic and fracture properties. The details of the calibration process are provided below. Since the experimentally reported stiffnesses and strengths are in GPa and the RVE size in Figure 2a is expressed in \(\upmu\)m, we use GPa and \(\upmu\)m as units of stiffness/ strength and length for the remainder of the paper. For multiphase composites, the volume fractions and topologies of individual phases contribute to the overall elastic and fracture properties of the material at a given SVE (observation) size. Herein, similar to [5; 9; 10], the additively manufactured material is treated as single-phase with the melt pool boundaries being the dominant feature responsible for a material nonlinear response. From this perspective, there are two aspects that contribute to the compliance of SLM material: bulk compliance and traction separation model compliance. This is due to the fact that the cohesive model is intrinsic; that is, it has the initial slope of \(k\) in Figure 6. To demonstrate the effect of cohesive model compliance, consider a one-dimensional domain, wherein equal length elastic regions of length \(L\) and elastic modulus \(E_{m}\) are separated by cohesive interfaces with initial stiffness \(k\).