• additive manufacturing
• powder bed fusion
• selective laser melting
• welding
• multi-scale modeling
• finite element simulation
• pointwise strain superposition
• Rosenthal solution
• process optimization
• misfit strain
• quasi-analytical modeling
• residual stress
• distortion

Residual stresses and distortions are key issues in Powder Bed Fusion (PBF) processes, affecting both the manufacturability and the mechanical strength of 3D printed parts. Their prediction via physical modeling could help reduce the number of failed iterations often needed before achieving a successful build.
The first part of this thesis concerns a multi-scale PBF simulation method composed of a meso-scale thermo-structural model, a macro-scale structural model, and a scaling strategy named Pointwise Strain Superposition. The method was capable of reproducing the process-induced stresses and distortions on selective laser melted Inconel 718 with first- or higher-order accuracy, despite the uncertainties regarding input parameters and material properties.
The final part of the thesis introduces a theoretical framework for the analysis and optimization of melting processes that use focused moving heat sources (including welding and PBF). Among the most significant findings are a closed-form procedure to determine the optimal operating condition given two geometric constraints on the melt isotherm and a quasi-analytical method to compute the residual stress field associated with the Rosenthal solution under the linearity assumption. This latter method is based on the concept of misfit strain (i.e., the inelastic strain induced by the gradient of thermal expansion at solidification), which could prove to be an instrumental expedient for modeling solidification in solid mechanics.