###### Abstract
Moreover, in [12; 13], researchers conduct a morphological analysis that directly assesses inherent physical traits, thereby reinforcing the substantial connection between processing parameters and the resulting material behavior. Even with the extensive literature outlining the effect of various process parameters and demonstrating the effects with approximated domains, there exists a gap in our understanding of the mechanical behavior at different length scales for metal SLM materials. In this work, a framework is introduced to employ a high-fidelity meshing approach to comprehensively represent the intricate complexities of SLM microstructures. Additionally, the variation in mechanical properties is examined across various length scales, elucidating the intricate connection between these fluctuations and specific regions within the melt pool. Numerical homogenization has proven to be an effective means to quantify material properties, given a microstructure with such complexities [14]. The goal of numerical homogenization is to upscale the effect of all microstructural details into the effective or apparent material properties that can be used in continuum-level models [15]. In homogenization theory, a representative volume element (RVE) refers to a large-enough domain for which a target material property can be considered converged versus the volume element size [16; 17; 18; 19]. There are various perspectives in defining convergence [20; 21; 22]. For example, one can examine if the given property is almost independent of the choice of boundary conditions used [23; 24], whether the mean value has stabilized versus the volume size, or whether the variation of the homogenized properties over a population of volume elements (VEs) of the same size is small  
Figure 1: Conceptual drawing of a melt pool [3]. enough [25; 26]. Depending on the mechanical properties in question, however, constructing an appropriately sized RVE can prove sufficiently challenging, if not impractical [26]. For example, fracture-related properties have very large RVE sizes. An alternative approach, one that attempts to consider the variability of the microstructure, is the concept of a statistical volume element (SVE), first introduced in [27; 28; 29] for homogenizing elastic properties. SVE homogenization partitions a large domain into VEs much smaller than the RVE size limit for a given property. Understanding the variation in mechanical properties versus VE (SVE) size and homogenizing properties in terms of SVEs, as opposed to RVEs, has multiple benefits. First, many mechanical properties have a specific form of size effect; that is, the trends in which the mean and variation in the given property change versus the observation (SVE) size [30; 31]. Second, RVE-based homogenization has been rendered ineffective in many fracture analyses as all material heterogeneities that play a key role in crack nucleation, propagation, and coalescence are lost in the homogenization process. For example, a lack of convergence or convergence to an incorrect value is reported for fracture pattern [32] and fracture energy [33]. In the method of moving window [34; 35], a window (SVE) traverses a macroscopic domain, and each time at the centroid of the SVE assigns the homogenized properties. Unlike RVEs, the homogenized values at different locations are not uniform (or almost uniform), hence the corresponding mesoscopic property fields generated are inhomogeneous and address the aforementioned problem. Third, many interesting mechanical responses of a material are stochastic. For example, for the same sample geometry and loading, different fracture patterns and strain-stress curves are reported in [36] and [37], respectively. The smaller size of SVEs (compared to RVEs) ensures that the homogenized properties are stochastic and maintain the mentioned sample-to-sample variation. In short, the SVE-based properties maintain a certain level of material heterogeneity and randomness, and are a promising tool in multiscale material modeling.