Sparse-projection eigenstrain tomography of complex additive manufacturing residual stresses

Full-field three-dimensional residual stress assessment in additively manufactured components remains a critical challenge in solid mechanics, owing to the complex nature of internal stress fields, limited experimental accessibility, and the high computational cost of transient thermomechanical simulations. To overcome this limitation, this study introduces a stable, physics-constrained inverse framework utilising sparse-projection eigenstrain tomography to assess a cubic laser powder bed fusion AlSi10Mg test specimen. While conventional synchrotron mapping requires days of acquisition, the proposed approach reconstructs voxel-parameterised incompatible strain fields and recovers the full six-component residual stress tensor from only two orthogonal projections. By mathematically embedding the continuum mechanics constraints of macroscopic force equilibrium and Saint-Venant strain compatibility, the fundamentally ill-posed inverse problem is rendered numerically stable. This work represents the successful full-tensor volumetric reconstruction from sparse projections in an additively manufactured component. This novel experimental reconstruction provides a rigorous physical dataset, which is evaluated against a transient non-linear thermomechanical finite element model. Both routes exhibit robust morphological agreement in reproducing the characteristic compressive interior and tensile vertical edges of the part. This qualitative validation reveals a critical physical distinction where the numerical model provides the idealised macroscopic continuum baseline, while the inverse tomography simultaneously captures and preserves sharp, localised micro-mechanical variations. By reducing the number of projections for volumetric evaluation, this framework provides a highly efficient and mathematically rigorous tool for complex residual stress analysis.