A robust implementation for 2D Digital Image Correlation

In this communication the inverse problem of reconstructing the in-plane (2D) displacements of a monitored surface through a sequence of two-dimensional digital images, severely ill-posed in Hadamard’s sense, is investigated. A novel variational formulation is presented for the continuum 2D Digital Image Correlation (2D DIC) problem, and critical issues such as semi-coercivity and solution multiplicity are discussed. In the framework of a Galerkin, finite element discretization of the displacement field, a robust implementation for 2D DIC is outlined, aiming to attenuate the spurious oscillations which corrupt the deformation scenario especially when very fine meshes are adopted. To this purpose, besides the multi-grid approach, recourse is made to a Tychonoff regularization provision, preserving the solution against an unstable response. The algorithm is assessed on the basis of both synthetic and truly experimental image pairs.