Inverse identification of inherent strain for efficient prediction of residual stress and deformation in wire arc additive manufacturing parts

Multi-pass and multi-layer wire arc additive manufacturing (WAAM) induces residual stress accumulation and geometric distortions, which can degrade dimensional accuracy and structural performance. The thermal elastic-plastic finite element method (TEP-FEM) can reproduce these responses in detail, but its high computational cost limits its application to large-scale structures. Although the inherent strain (IS) method provides an efficient alternative based on linear elastic analysis, its accuracy strongly depends on the prescribed IS distribution. This study develops an inverse IS identification method to determine separate IS values for individual deposition passes or layers in WAAM-fabricated structures from limited measurement data. Displacement, strain, or stress data can be used within the same inverse analysis workflow according to practical measurement availability. The method is assessed through benchmark verification using prescribed IS values, TEP-FEM-based reproduction, substrate-removal prediction, and experimental data-based validation with noise sensitivity analysis. In the preset-IS benchmark cases, the average deviations between the identified and prescribed IS values are 0.17% for a planar cladding structure (PCS) and 0.47% for a thin-wall structure (TWS). For the TEP-FEM-based TWS, the reproduced longitudinal stress agrees well with the reference result, with a coefficient of determination R 2 of 0.9922. The identified IS can also predict the dominant stress redistribution and final deformation tendency after substrate removal. Furthermore, the proposed inverse IS identification method is validated using a part of experimentally measured residual stress data obtained by the contour-method and achieves a good accuracy with the mean absolute error of 4.21 MPa and an R 2 of 0.9988. Under 5% input noise, the validation R 2 remains 0.9950 ± 0.0008. The inverse IS identification method reduces the computation time by more than two orders of magnitude compared with the corresponding TEP-FEM stress analyses. These results indicate that the proposed method provides a practical route for efficient residual stress and deformation prediction in WAAM-fabricated structures using limited measurement data.