An Optimization Framework for Identifying Non-Uniform Elastic–Plastic Residual Stresses from Central Hole-Drilling

The incremental hole-drilling method overestimates residual stress as they approach the material yield limit (typically above ~60% of the yield strength), primarily due to localized plastic deformation around the drilled cavity. Existing correction methods commonly assume depth-invariant stress distributions, limiting their applicability to components with steep residual stress gradients. This study formulates the residual stress reconstruction problem as an inverse optimization framework to recover the underlying elastic–plastic stress state. An automated procedure iteratively updates boundary conditions in a three-dimensional finite element model until simulated strain relaxations match experimental strain gauge measurements. The model employs a representative volume with locally refined mesh density near the hole and gauge locations, while incremental material removal is simulated via sequential element deactivation to replicate the drilling process. To ensure numerical stability and physically admissible solutions, stress bounds are imposed to restrict the solution space to valid multiaxial states. By explicitly incorporating elastic–plastic material behavior within each iteration of the inverse optimization, the proposed approach directly captures localized yielding and its influence on strain relaxation. This eliminates the inaccuracies associated with linear-elastic assumptions and enables accurate identification of depth-varying residual stress fields near the material’s yield limit.