A regularized finite-element digital image correlation for irregular displacement field

• The displacement field can be computed accurately with small element size.
• The displacement field can have fine and irregular structure.
• The algorithm is accurate and robust even for irregular displacement field.
• No a priori information is necessary for the regularization.

A nonlinear Tikhonov regularization scheme is developed to tackle the ill-posed finite-element digital image correlation, which aims to measure the displacement field from consequent digital images before and after deformation. The goal of this algorithm is to resolve the displacement field with fine and irregular structure without deteriorated by the measuring errors due to its ill-posedness. A Newton-type method is employed to linearize the nonlinear problem iteratively, then the Tikhonov regularization is applied to the linearized problem, with the regularization parameter adaptively chosen by the L-curve method. The proposed algorithm is verified by computer simulated input images with a priori displacement field. The result shows that it is capable of resolving displacement field with very fine structure in a reasonable accuracy.