## 2 Materials and Methods
Accordingly, \(L_{SVE}=56\) is the minimum size below which there will be less than one melt pool on average within a SVE. As a sub-melt pool length scale, the model ideally should incorporate grain-level mechanisms, crystal plasticity, or other alternative physics-based models more appropriate for investigating the failure response of the SVE. In the following, we use a cohesive model to model failure between the melt pools. Accordingly, due to the lack of more accurate grain-scale models in this work, we limited the smallest SVE size to \(L_{SVE}=56\). As for the largest size, SVEs larger than \(L_{SVE}=140\)\(\upmu\)m would result in fewer than 36 SVEs, which may be a too small number to accurately calculate the mean and standard deviation of homogenized properties. We refer the reader to [26] on why this is especially a concern for fracture properties due to their slower convergence relative to \(L_{SVE}\) compared with that of elastic properties. In short, while ideally we could model larger SVEs (if starting with a larger experimental image, as shown in Figure 2a), the chosen sizes still manifest distinct mechanical behaviors. Larger sizes are valuable for revealing interactions between multiple melt pools, while mid-range sizes shed light on interactions between select boundaries. The microstructure and the corresponding conforming mesh for one of the SVEs with \(L_{SVE}=140\)\(\upmu\)m are illustrated in Figure 5b. For reference, the CISAMR mesh is generated on a background structured mesh with an element size of 2.8 \(\upmu\)m, with two levels of \(h\)-adaptive refinement along melt pool boundaries. Accordingly, the SVEs of sizes \(L_{SVE}=56\), 84, 112, and 140 \(\upmu\)m correspond to 20, 30, 40, and 50 background elements along the edge, respectively. The calibration of material and interface properties and finite element analysis of the SVEs are discussed next. Figure 4: Modifications in the original CISAMR algorithm to handle the presence of sharp corners along material interfaces. Blue, red, and yellow nodes correspond to sharp corners of the material interface, hanging nodes created during the SAMR process, and conforming background mesh nodes, respectively. Figure 5: (**a**) The microstructure of the SLM material. Each color representing a unique melt pool; (**b**) a sample SVE extracted from CISAMR mesh generated on the domain in (**a**), with an inset showing the mesh structure. Finite element analysis by Abaqus [42] was used to analyze the derived SVEs under three different load cases to characterize the response for tensile loading in vertical and horizontal directions (denoted by \(v\) and \(h\) subscripts), and shear loading. The most common boundary conditions (BCs) for the homogenization of elastic properties are the kinematic uniform boundary condition (KUBC) and stress uniform boundary condition (SUBC). In the KUBC, two displacements of the boundary nodes are specified as consistent with a macroscopic strain tensor. In the SUBC, traction values corresponding to a constant macroscopic stress tensor are applied on the boundary of VE. KUBC and SUBC provide the upper and lower limits for the homogenized elastic properties, with the properties converging to unique values as the SVE size increases [43; 44; 45]. The KUBC is not appropriate for the nonlinear failure problem as it does not permit a crack to completely tear vertically or horizontally through the domain. The SUBC is also not appropriate for failure simulations as it cannot model the unloading portion of the homogenized strain-stress response. We have used a mixed boundary condition (MBC) [26] for homogenization. The MBC condition is preferred over the KUBC and SUBC for multiple reasons. First, the homogenized elastic properties are in between the KUBC and SUBC values and thus are not overly over- or under-estimated for small SVE sizes. Second, it allows cracks to completely go through the VE and can model the unloading portion of the strain-stress response, and the problems of KUBC and SUBC, respectively.