Classic and Inverse Compositional Gauss-Newton in Global DIC

Jean-Charles Passieux (1) , Robin Bouclier (2, 1)

1 ICA - Institut Clément Ader
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Today, effective implementations of Digital Image Correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic Finite Element (or more generally global) DIC (FE-DIC) solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution...) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then an Inverse Compositional Gauss-Newton (ICGN) implementation of FE-DIC is proposed as a cost effective and mathematically sound alternative to this approximation.

Mots clés: inverse compositional Gauss-Newton; global DIC; forward compositional Gauss-Newton

Domaines: Mécanique des structures [physics.class-ph]

Jean-Charles Passieux, Robin Bouclier. Classic and Inverse Compositional Gauss-Newton in Global DIC. International Journal for Numerical Methods in Engineering, inPress, 119 (6), pp.453-468. ⟨10.1002/nme.6057⟩. ⟨hal-02059472⟩