Radial basis point interpolation for strain field calculation in digital image correlation

• Jiayi Du, ZHAO JIAN, Jiahui Liu, and Dong Zhao
• received 01/29/2024; accepted 04/17/2024; posted 04/17/2024; Doc. ID 520232
• Abstract: In order to extract smooth and accurate strain fields from the noisy displacement fields obtained by digital image correlation (DIC), a point interpolation meshless (PIM) method with radial basis function (RBF) is introduced for full-field strain calculation, which overcomes the problems of slow calculation speed and unstable matrix inverse calculation of the element-free Galerkin method (EFG). The radial basis point interpolation method (RPIM) with three different radial basis functions and the moving least squares (MLS) and pointwise least squares (PLS) methods are compared by analyzing and validating the strain fields with high strain gradients in simulation experiments. The results indicate that RPIM is nearly 80% more computationally efficient than the MLS method when a larger support domain is used, and the efficiency of RPIM is nearly 26% higher than that of the MLS method when a smaller support domain is used; the strain calculation accuracy is slightly lower than that of the MLS method by 0.3-0.5%, but the stability of the calculation is significantly improved. Different from the PLS method, which is easily affected by the noise and the size of the strain calculation window, RPIM is insensitive to the displacement noise and the size of the support domain and can obtain similar calculation accuracy. RPIM with Multiquadric (MQ) radial basis functions perform well in balancing computational accuracy and efficiency and is insensitive to shape parameters. Application cases show that the method can effectively compute the strain field at the crack tip, validating its applicability to the study of the plastic region at the crack tip. In conclusion, the proposed RPIM-based method provides an accurate, practical, and robust approach for full-field strain measurements.