A modified stress function approach is developed for reconstruction of residual stress and eigenstrain fields from limited experimental measurements. The modified approach is successfully applied to three experimental case studies where residual stresses are introduced by surface peening. The smooth reconstructed residual fields not only minimize the deviation of measurements from its approximation but also satisfy all continuum mechanics requirements. Furthermore, a comprehensive discussion is performed on regularity of the solution in Tikhonov scheme and the regularization parameter is then determined utilizing Morozov discrepancy principle. Newton iterative method is also shown to have an excellent fast convergence to the regularization parameter while effectively reduces the computational cost.
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