Determination of the mechanical properties of additively manufactured structures with random microstructural defects

This work presents a computational framework for the stochastic modeling of structures additively manufactured using the Fused Deposition Modeling (FDM) technique. In particular, it investigates the random spatial variation of elastic properties in 3D printed structures, which originates from random microstructural defects caused by geometric irregularities in pore formation due to deviations in filament placement. Initially, the moving window technique is employed to generate stochastic mesoscale models by extracting statistical volume elements (SVEs) from digital images. Each SVE is then analyzed through the extended finite element method (XFEM), allowing the accurate modeling of material discontinuities without the need for remeshing. Computational homogenization is applied under kinematically uniform boundary conditions (KUBCs) and statically uniform boundary conditions (SUBCs) to compute the apparent constitutive tensor of the 3D printed structure. Macroscopic stresses and strains are calculated as volume integrals of the corresponding microscopic fields, ensuring satisfaction of the Hill-Mandel energy condition. The methodology further incorporates spatial correlation analysis to capture the dependencies between the random fields of porosity and mechanical properties. The proposed framework provides an accurate stochastic description of the mechanical behavior of 3D printed structures, enabling efficient uncertainty quantification and improved predictive capability for structural applications.