Emerging crack front identification from tangential surface displacements

Stéphane Andrieux; Thouraya Nouri Baranger

doi:10.1016/j.crme.2012.06.002

Emerging crack front identification from tangential surface displacements

Stéphane Andrieux ¹ ; Thouraya Nouri Baranger ²

¹ LaMSID, UMR CNRS-EDF 2832, 1, avenue du Général de Gaulle, 92141 Clamart cedex, France
² Université de Lyon, CNRS, Université Lyon 1, LaMCoS UMR5259, 69621 Villeurbanne cedex, France

Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 565-574.

Résumé
Abstract

On présente dans cette Note une méthode dʼidentification du front dʼune fissure débouchant à la surface dʼun solide élastique, à partir de la donnée des composantes tangentielles du champ de déplacement sur une partie libre de charge de la surface extérieure. La méthode comporte deux étapes. Dans un premier temps, on résoud un problème de Cauchy pour prolonger le champ en surface jusquʼà une surface englobant la fissure inconnue. Dans une seconde étape, on utilise la méthode dʼécart la réciprocité pour identifier le saut de déplacement à la traversée de la fissure, ce qui conduit, par lʼidentification du support, à lʼidentification de la fissure elle-même. On prouve ainsi un résultat dʼidentifiabilité. La méthode est illustrée sur deux exemples synthétiques : une fissure traversante à front rectiligne et une fissure elliptique débouchante.

We present in this Note an identification method for the crack front of a crack emerging at the surface of an elastic solid, provided displacements field or its tangential components are given on a part free of loading of the external surface. The method is based on two steps. The first one is the solution of a Cauchy problem in order to expand the displacement field within the solid up to a surface enclosing the unknown crack. Then the reciprocity gap method is used in order to determine the displacement jump on the crack and then the crack itself. We prove then an identifiability result. The method is illustrated with two synthetic examples: a crossing crack with linear crack front and an elliptic emerging crack.

Reçu le : 2012-05-09
Accepté le : 2012-06-11
Publié le : 2012-07-04

DOI : 10.1016/j.crme.2012.06.002

Keywords: Solids and structures, Inverse problem, Crack identification, Cauchy problem, Elasticity, Full-fields measurements, Data completion
Mots clés : Solides et structures, Problèmes inverses, Identification de fissure, Problème de Cauchy, Elasticité, Mesures de champs, Complétion de données

Affiliations des auteurs :

Stéphane Andrieux ¹ ; Thouraya Nouri Baranger ²

¹ LaMSID, UMR CNRS-EDF 2832, 1, avenue du Général de Gaulle, 92141 Clamart cedex, France
² Université de Lyon, CNRS, Université Lyon 1, LaMCoS UMR5259, 69621 Villeurbanne cedex, France

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     author = {St\'ephane Andrieux and Thouraya Nouri Baranger},
     title = {Emerging crack front identification from tangential surface displacements},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {565--574},
     publisher = {Elsevier},
     volume = {340},
     number = {8},
     year = {2012},
     doi = {10.1016/j.crme.2012.06.002},
     language = {en},
}

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Stéphane Andrieux; Thouraya Nouri Baranger. Emerging crack front identification from tangential surface displacements. Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 565-574. doi : 10.1016/j.crme.2012.06.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.06.002/

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