Identification of internal cracks in a three-dimensional solid body via Steklov–Poincaré approaches

Mohamed Larbi Kadri; Jalel Ben Abdallah; Thouraya Nouri Baranger

doi:10.1016/j.crme.2011.06.004

Identification of internal cracks in a three-dimensional solid body via Steklov–Poincaré approaches

Mohamed Larbi Kadri ¹; Jalel Ben Abdallah ¹ ; Thouraya Nouri Baranger ²

¹ Université El Manar, LAMSIN, École nationale dʼingénieurs de Tunis, BP no. 37, 1002 Tunis, Tunisia
² Université de Lyon, CNRS, université Lyon 1, LaMCoS UMR 5259, INSA-Lyon, 18-20, rue des sciences, 69621 Villeurbanne cedex, France

Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 674-681.

Abstract
Résumé

This Note deals with the identification of internal planar cracks inside a three-dimensional elastic body via two approaches relying on domain decomposition using elastostatic measurements. These approaches consist in recasting the problem in terms of primal or dual Steklov–Poincaré equations. The primal approach is a straightforward continuation to the elastic Cauchy problem of the work presented in J. Ben Abdallah (2007) [1] which is devoted to the Cauchy problem for the scalar Laplace equation. The numerical performances of these formulations are compared.

Cette Note concerne la résolution numérique du problème dʼidentification de fissures planes dans un solide élastique tridimentionnel, via deux approches issues de la décomposition de domaine, à lʼaide de mesures élastostatiques. Ces approches consistent à reformuler le problème en termes dʼéquations de Steklov–Poincaré primale et duale. Lʼapproche primale a fait lʼobjet dʼune étude numérique dans le cadre de lʼéquation de Laplace J. Ben Abdallah (2007) [1]. Les performances numériques des deux approches sont comparées entre elles.

Received: 2010-11-25
Accepted: 2011-06-24
Published online: 2011-07-30

DOI: 10.1016/j.crme.2011.06.004

Keywords: Computational solid mechanics, Crack identification, Data completion, Inverse problem, Cauchy problem, Steklov–Poincaré equations
Mots-clés : Mécanique des solides numérique, Identification de fissures, Complétion de données, Problème inverse, Problème de Cauchy, Équations de Steklov–Poincaré

Author's affiliations:

Mohamed Larbi Kadri ¹; Jalel Ben Abdallah ¹; Thouraya Nouri Baranger ²

¹ Université El Manar, LAMSIN, École nationale dʼingénieurs de Tunis, BP no. 37, 1002 Tunis, Tunisia
² Université de Lyon, CNRS, université Lyon 1, LaMCoS UMR 5259, INSA-Lyon, 18-20, rue des sciences, 69621 Villeurbanne cedex, France

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     author = {Mohamed Larbi Kadri and Jalel Ben Abdallah and Thouraya Nouri Baranger},
     title = {Identification of internal cracks in a three-dimensional solid body via {Steklov{\textendash}Poincar\'e} approaches},
     journal = {Comptes Rendus. M\'ecanique},
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Mohamed Larbi Kadri; Jalel Ben Abdallah; Thouraya Nouri Baranger. Identification of internal cracks in a three-dimensional solid body via Steklov–Poincaré approaches. Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 674-681. doi : 10.1016/j.crme.2011.06.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.06.004/

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