Classic and inverse compositional Gauss‐Newton in global DIC. (27th March 2019)

• Record Type: Journal Article
• Authors: Passieux, Jean‐Charles; Bouclier, Robin
• Is Part Of: International journal for numerical methods in engineering. Volume 119:Number 6(2019)
• Page Start: 453
• Page End: 468
• Publication Date: 2019-03-27
• Subjects: forward compositional Gauss‐Newton -- global DIC -- inverse compositional Gauss‐Newton; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6057
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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 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, etc) 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 implementation of finite element DIC is proposed as a cost‐effective and mathematically sound alternative to this approximation.