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Laser-powder bed fusion additive manufacturing (LPBF-AM) of metals is rapidly becoming one of the most important materials processing pathways for next-generation metallic parts and components in a number of important applications. However, the large parametric space that characterizes laser-based LPBF-AM makes it challenging to understand what are the variables controlling the microstructural and mechanical property outcomes. Sensitivity studies based on direct LPBF-AM processing are costly and lengthy to conduct, and are subjected to the specifications and variability of each printer. Here we develop a fast-throughput numerical approach that simulates the LPBF-AM process using a cellular automaton model of dynamic solidification and grain growth. This is accompanied by a polycrystal plasticity model that captures grain boundary strengthening due to complex grain geometry and furnishes the stress-strain curves of the resulting microstructures. Our approach connects the processing stage with the mechanical testing stage, thus capturing the effect of processing variables such as the laser power, laser spot size, scan speed, and hatch width on the yield strength and tangent moduli of the processed materials. When applied to pure Cu and stainless 316L steel, we find that laser power and scan speed have the strongest influence on grain size in each material, respectively.