Thermoelastic analogy-based finite element framework for full-field residual stress reconstruction

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Accurate characterization of residual stress distributions is critical for evaluating structural integrity, service reliability, and mechanical performance. Existing experimental techniques are mainly limited to pointwise measurements, whereas indirect methods typically rely on uncertain prior assumptions and often lack subsequent applicability. To address these limitations, this study proposes a finite element (FE)-compatible framework for reconstructing full-field residual stresses from discrete measurements. Specifically, an auxiliary pseudo-temperature field is introduced via a thermoelastic analogy to parameterize an equivalent isotropic eigenstrain source. On this basis, thermoelastic response matrices are constructed by applying unit pseudo-temperature inputs to individual elements in the FE forward model. The pseudo-temperature field is then identified using Tikhonov regularization with stability-constrained generalized cross-validation and reintroduced into the forward model to reconstruct full-field residual stresses that inherently satisfy equilibrium and compatibility. Across three numerical examples, the framework achieves high-fidelity reconstruction with different element orders and numerical integration schemes, while maintaining stable performance under reduced sampling and measurement noise. Results spanning distinct geometric configurations and residual stress generation mechanisms further demonstrate the framework’s broad applicability to structures amenable to standard FE discretization. The reconstructed stress field can be directly incorporated into commercial FE software for subsequent analyses.