Analytical Approach for Inverse Reconstruction of Eigenstrains and Residual Stresses in Autofrettaged Spherical Pressure Vessels

The stress function approach is revisited for the inverse determination of residual stresses and eigenstrains from limited pointwise data in spherically symmetric stress state. The robust least squares technique is utilized to minimize the deviation of the measurement data from the model predictions while a full range of continuum mechanics requirements are satisfied. The application of the newly proposed spherical stress function is effectively demonstrated for two cases of analytical and numerical solutions considering different material behavior models. Also, the eigenstrains are inversely determined satisfying the equation of strain compatibility and a closed form analytical solution is presented.