Comptes Rendus
no. 6
Identification of elastic parameters by displacement field measurement
[Identification de paramètres mécaniques par mesure de champ de déplacement]
Giuseppe Geymonat1 ; François Hild2 ; Stéphane Pagano1
1 LMGC, CNRS–Université de Montpellier II, place E. Bataillon, CC048 34005 Montpellier cedex, France
2 LMT-Cachan, ENS de Cachan/CNRS UMR 8535/Université Paris 6, 61, avenue du Président Wilson, 94235 Cachan cedex, France
Comptes Rendus. Mécanique, Volume 330 (2002) no. 6, pp. 403-408.

On étudie un problème d'identification de paramètres associés à des équations de la mécanique en dimension 2. Pour cela, dans une première partie, on présente le procédé expérimental permettant de mesurer le champ de déplacements. La méthode variationnelle proposée est basée sur la minimisation d'une fonctionnelle séparement convexe et permet de reconstruire à la fois le tenseur d'élasticité et le champ des contraintes à partir des mesures du champ de déplacements. Les deux champs reconstruits sont continus et linéaires par morceaux sur une triangulation du domaine bidimensionnel. Pour tester les performances de l'algorithme on présente des exemples numériques et expérimentaux.

In this Note we study a parameter identification problem associated with a two-dimensional mechanical problem. In a first part, the experimental technique of determining the displacement field is presented. The variational method proposed herein is based on the minimization of a separate convex functional which leads to the reconstruction of the elastic tensor and the stress field. These two reconstructed fields are continuous and piecewise linear on a triangulation of the two-dimensional problem. Some numerical and experimental examples are presented to test the performance of the algorithm.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(02)01476-6
Keywords: continuum mechanics, identification, inverse problem, digital image correlation
Mots-clés : milieux continus, identification, problème inverse, corrélation d'images numériques

Giuseppe Geymonat 1 ; François Hild 2 ; Stéphane Pagano 1

1 LMGC, CNRS–Université de Montpellier II, place E. Bataillon, CC048 34005 Montpellier cedex, France
2 LMT-Cachan, ENS de Cachan/CNRS UMR 8535/Université Paris 6, 61, avenue du Président Wilson, 94235 Cachan cedex, France 
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Giuseppe Geymonat; François Hild; Stéphane Pagano. Identification of elastic parameters by displacement field measurement. Comptes Rendus. Mécanique, Volume 330 (2002) no. 6, pp. 403-408. doi : 10.1016/S1631-0721(02)01476-6. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01476-6/

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