Chapter 3 IGMU: A Geometrically Consistent Framework for Identification from Full Field Measurement J.-E. Dufour, J. Schneider, F. Hild, and S. Roux Abstract DIC can be coupled with computational tools in order to characterize materials by using identification techniques such as finite element model updating or integrated approaches. In this study a framework using CAD-based stereo-DIC coupled with Isogeometric Analyses is followed to implement such identification procedures. Using both techniques allows us to be consistent with the designed geometry and its kinematics as the NURBS formalism is kept during the whole process and fewer degrees of freedom are needed (for the displacement field and the geometric representation of the surfaces) than in classical (finite element) approaches. This technique can be adapted to be written within an integrated framework (whose sensitivity fields are given by an isogeometric code). Keywords CAD representation • DIC • Global approach • Identification • Stereo-correlation 3.1 Introduction Identification from full-field measurement is widely used in the experimental mechanics field to calibrate material parameters. Techniques such as Finite Element Model Updating (FEMU) [1] or Integrated Digital Image Correlation (I-DIC) [2] can be used to extract these parameters from the coupling of numerical and experimental results. The present work is dedicated to the development of an identification method coupling CAD-Based Stereo-DIC [3] and Isogeometric Analyses [4] in a framework similar to FEMU to identify material parameters. These techniques provide a geometrically consistent framework and a reduced kinematic basis as Non-Uniform Rational B-Splines (NURBS [5]) are used during the whole process. Such type of approach will also be extended into an integrated DIC framework. The outline of the paper is as follows. First, a virtual experiment is created. Second, the principle of the so-called IsoGeometric Model Updating (IGMU) framework is introduced. Last, the concept of Integrated CAD-based Stereo-DIC is explained and the same experiment is used to show the feasibility of such an approach. 3.2 Virtual Experiment for Identification Porpuses In order to test the developed identification procedure, a simple virtual case is designed. Using an isogeometric analysis code [6], a tensile test is simulated on a virtual beam sample (Fig. 3.1a). Pictures for the correlation analyses are then created (Fig. 3.1b) by projecting two faces of the beam onto 2D image planes using known projection matrices [7] and virtually applying a gray level pattern on the considered surfaces. In the present setting, four pictures are computed for each considered loading step of this virtual experiment. J.-E. Dufour (*) LMT Cachan, ENS Cachan/CNRS UMR 8535/University Paris Saclay, 61 Avenue du Pre´sident Wilson, Cachan 94235, France SAFRAN Snecma Villaroche, Rond-point Rene´ Ravaud, Re´au 77550, France e-mail: dufour@lmt.ens-cachan.fr J. Schneider SAFRAN Snecma Villaroche, Rond-point Rene´ Ravaud, Re´au 77550, France F. Hild • S. Roux LMT Cachan, ENS Cachan/CNRS UMR 8535/University Paris Saclay, 61 Avenue du Pre´sident Wilson, Cachan 94235, France #The Society for Experimental Mechanics, Inc. 2016 S. Bossuyt et al. (eds.), Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-21765-9_3 17
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