Eigenstrain tomography for robust reconstruction of residual stresses from noisy polycrystalline diffraction projections with Tikhonov-type Laplacian smoothing

Residual stress reconstruction from high-energy diffraction data is often compromised by noise and outliers arising from poor grain statistics in polycrystalline measurements. This study introduces a robust workflow in which quadratic Tikhonov-type Laplacian smoothing is applied directly to lattice-strain projection data prior to mechanics-informed eigenstrain tomography. Although the eigenstrain framework can incorporate all tensor components of measured strain, a deliberately minimal and experimentally economical implementation is demonstrated using only the axial lattice-strain component from two orthogonal projections of a water-quenched AA6082 aluminium bar. The influence of the smoothing parameter on the reconstructed three-dimensional stress field is examined systematically to distinguish genuine quench-induced stress gradients from noise-driven spatial oscillations. A physics-informed admissibility criterion is introduced to select this parameter by constraining the reconstructed peak von Mises stress within the tensile strength limits of the quenched material. This approach suppresses non-physical high-frequency artefacts while preserving the macroscopic Type I residual stress distribution, thereby improving robustness to experimental noise without addressing the fundamental non-uniqueness of the inverse eigenstrain problem under limited measured components.