Residual stress prediction across dimensions using improved radial basis function based eigenstrain reconstruction

Accurate prediction of residual stress has significant impacts on structural fatigue and long-term performance. Eigenstrain reconstruction emerges as a competitive method for residual stress prediction, due to the appealing engineering adaptability and cost effectiveness. However, traditional eigenstrain methods, by polynomial forms, have difficulties in reconstructing residual stress with complex contour. In such cases, high-order polynomials have to be used to enhance reproduction capability within the domain. Unfortunately, polynomial interpolation with high degree over a set of measurements often encounters unexpected numerical oscillation, known as the Runge's phenomenon. This numerical limitation will misinterpret the residual stress with abrupt change or near the boundary of structures. To tackle these limitations, this paper investigates the residual stress prediction across dimensions. An eigenstrain reconstruction method based on radial basis function (RBF) is proposed in this work. By virtue of least squares method, full-field residual stress can be reproduced by solving an inverse eigenstrain problem through minimizing the residual errors between numerical predictions and experimental measurements. The radial basis function is used as the basis function space to reconstruct the full scale eigenstrain, and then the residual stress in three different dimensions. More importantly, a novel elliptical radial basis function has been proposed for predicting welding residual stress. Thanks to the unique scatter interpolation feature of radial basis function with limited experimental data, the distinctive advantage of the proposed method lies in the excellence of accurately predicting complex residual stresses in one dimension, the whole two dimensions or even three-dimensional components. The eigenstrain reconstruction method based on radial basis function enriches residual stress prediction with complex profiles in two-dimensional and three-dimensional space.