Theoretical and Numerical Analyses of Systematic Errors in Local Deformations

Abstract

There are displacement systematic errors due to undermatched shape functions and strain systematic errors due to undermatched surface fitting functions using the digital image correlation (DIC) method. The measured displacement and strain results are heavily affected by the calculation parameters (such as the subset size, the grid step, and the strain window size) due to undermatched shape functions and surface fitting functions. To evaluate the systematic errors, theoretical and numerical analyses of displacement and strain systematic errors have been carried out when the first- and second-order shape functions, and the quadric surface fitting functions are used. When the forth-order Taylor expansion is employed for the displacement, the results come out: (1) the approximate displacement systematic errors are functions of the second- and forth-order displacement gradients when first- and second-order shape functions are used, respectively; (2) the approximate strain systematic errors are functions of the third-order displacement gradients when first-order shape functions are used, and functions of the third- and fifth-order displacement gradients when second-order shape functions are used.