A weak-form method for strain field calculation with digital image correlation

Abstract

In digital image correlation (DIC), iterative spatial-domain cross-correlation algorithms have been routinely used to extract displacement fields from the recorded images. Then, strain fields are computed from the noisy displacement fields by a proper numerical different approach, like pointwise least squares fitting, which is tricky in choosing optimal calculation parameters. This work proposes an alternative weak-form framework to calculate strain fields from noisy displacement measurements by DIC. While direct numerical differentiation may amplify the noise in the displacement fields, the proposed method transfers differentiation into integration by employing the idea of the weak-form, which is the foundation of modern computational mechanics. By selecting cosine series as trial/test functions and employing their orthogonality, a semi-analytical formula for calculating the strain field is given. Moreover, the Filon's method is used in this study to improve the accuracy of numerical integration as sinusoidal terms are involved. The effectiveness of the proposed method is verified by numerical examples. It is found that the proposed method is comparable to the famous PLS algorithm when it is for simple strain fields, while it is better in accuracy and its insensitivity to noise when large-gradient or highly-oscillating strain fields are to be measured.