Comptes Rendus
Identification of damage fields using kinematic measurements
[Identification de champs d'endommagement à l'aide de mesures cinématiques]
Comptes Rendus. Mécanique, Volume 330 (2002) no. 11, pp. 729-734.

It is proposed to determine damage fields on the surface of a material by using only full-field displacement measurements. A finite element approach is developed for which the unknown damage field is assumed to be piece-wise constant. Two examples are discussed in which the displacement field is either obtained by finite element analyses or measured by digital image correlation.

À partir de mesures de champs de déplacement exclusivement, il est proposé d'identifier des champs d'endommagement à la surface du matériau. Une formulation aux éléments finis est développée pour laquelle le champ d'endommagement est supposé constant par morceaux. Dans les deux exemples traités, le champ de déplacement est soit obtenu par un calcul aux éléments finis soit mesuré par corrélation d'images numériques.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(02)01524-3
Keywords: damage, identification, inverse problem, full-field measurements
Mots-clés : endommagement, identification, problème inverse, mesures de champs

Damien Claire 1, 2 ; François Hild 2 ; Stéphane Roux 1

1 Laboratoire “surface du verre et interfaces”, UMR CNRS/Saint Gobain, 39, quai Lucien Lefranc, 93303 Aubervilliers 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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     title = {Identification of damage fields using kinematic measurements},
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Damien Claire; François Hild; Stéphane Roux. Identification of damage fields using kinematic measurements. Comptes Rendus. Mécanique, Volume 330 (2002) no. 11, pp. 729-734. doi : 10.1016/S1631-0721(02)01524-3. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01524-3/

[1] Photomécanique (Y. Berthaud; M. Cottron; J.-C. Dupré; F. Morestin; J.-J. Orteu; V. Valle, eds.), 2001 (GAMAC, 2001)

[2] Advanced Optical Methods and Applications in Solid Mechanics (A. Lagarde, ed.), Kluwer, 2000

[3] H.D. Bui; A. Constantinescu Spatial localization of the error of constitutive law for the identification of defects in elastic solids, Arch. Mech, Volume 52 (2000), pp. 511-522

[4] G. Geymonat; F. Hild; S. Pagano Identification of elastic parameters by displacement field measurement, C. R. Mecanique, Volume 330 (2002), pp. 403-408

[5] R.V. Kohn; B.D. Lowe A variational method for parameter identification, Math. Mod. Numer. Anal, Volume 22 (1988), pp. 119-158

[6] P. Ladevèze; D. Nedjar; M. Reynier Updating of finite element models using vibration tests, AIAA, Volume 32 (1994), pp. 1485-1491

[7] M. Grédiac Principe des travaux virtuels et identification, C. R. Acad. Sci. Paris Sér. II, Volume 309 (1989), pp. 1-5

[8] M. Grédiac; E. Toussaint; F. Pierron L'identification des propriétés mécaniques de matériaux avec la méthode des champs virtuels, une alternative au recalage par éléments finis, C. R. Mecanique, Volume 330 (2002), pp. 107-112

[9] H.D. Bui Sur quelques problèmes inverses élastiques en mécanique de l'endommagement, C. R. Colloq. Nat. Calc. Struct. Hermes, Volume 1 (1995), pp. 25-35

[10] M. Ikehata Inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection, SIAM J. Appl. Math, Volume 50 (1990), pp. 1635-1644

[11] J. Lemaitre; J.-L. Chaboche Mechanics of Solid Materials, Cambridge University Press, 1990

[12] D. Claire; S. Roux; F. Hild Identification de conductivités thermiques et de propriétés élastiques locales par analyse de champs, Méca. Ind (2002) (soumis)

[13] F. Hild, CORRELILMT: A software for displacement field measurements by digital image correlation, Report 254, LMT-Cachan, 2002

[14] J.-N. Périé; S. Calloch; C. Cluzel; F. Hild Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model, Exp. Mech (2002) (in press)

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