3Non-invasive Spline-based Regularization of FE Digital Image Correlation Problems

3.1. Brief introduction

In this last chapter, we turn to the resolution of higher-level problems of optimization-type (also characterized as inverse problems). Thanks to its ability to look for the solution in a regular reduced subspace, IGA appears all the more relevant in this area, because it not only allows more efficiency in the computation but also provides a natural regularization framework compared to the roughness of the standard FE modeling that usually leads to ill-posed optimization problems. In other words, IGA offers the opportunity to play with only few control points to prescribe important yet smooth modifications of the considered quantity, while the FE modeling would probably lead to wiggly and irregular modifications. More precisely, we focus here on digital image correlation (DIC) in the context of experimental solid mechanics. DIC allows us to measure a displacement field from several images taken at different loading increments of an experimental test. In view of making use of these measured fields to perform data assimilation, a recent trend in this field, called FE-DIC, consists of considering for the discretization the analysis-suitable FE mesh; i.e. the refined FE mesh that allows us to accurately capture the mechanical solution from simulation software. This results in an inverse DIC problem that is highly ill-posed: the measured FE field generally contains too many ...

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