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Constitutive law misfit functional for cavities identification
1 : Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur
(LAMSIN)
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Website
Le Belvédère BP 37 1002 Tunis -
Tunisia
2 : École Centrale de Lyon
(ECL)
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Website
Ministère de l'Enseignement Supérieur et de la Recherche Scientifique, Université de Lyon
36 avenue Guy de Collongue - 69134 Ecully cedex -
France
The aim of this work is an analysis of a geometric inverse problem related to the identification of defaults, namely cavities in structures. The approach proposed in treating such problem is to transform it into a shape optimization one by the means of an error functional that can be interpreted as a constitutive law misfit functional. Moreover, this cost functional whose shape derivative is explicitly determined allows the implementation of a numerical minimization algorithm using the gradient information combined with the level set method. The efficiency of the proposed approach is highlighted by numerical results.
