Comptes Rendus
no. 7-8
Topological sensitivity of energy cost functional for wave-based defect identification
[Gradient topologique d'une fonction-coût énergétique pour l'identification de défauts en élastodynamique]
Marc Bonnet1
1 Laboratoire de mécanique des solides (UMR CNRS 7649), École polytechnique, 91128 Palaiseau cedex, France
Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 377-389.

Cet article porte sur la formulation du champ de gradient topologique (GT), correspondant à l'apparition de petites inclusions virtuelles dans le milieu, d'une fonction-coût de type énergétique. Cette dernière quantifie l'écart entre deux états élastodynamiques en régime fréquentiel (respectivement définis en termes de données de type Dirichlet ou Neumann sur la frontière pour des situations d'identification exploitant la possession de données aux limites surabondantes) comme l'énergie de déformation de leur différence. Ce type de fonction-coût constitue une forme particulière d'erreur en relation de comportement et peut être utilisée par exemple pour l'identification de défauts. Le GT est exprimée en termes de quatre champs élastodynamiques, à savoir les champs libre et adjoint associés à chaque type de données aux limites. Un résultat similaire est également donné pour le cas de l'acoustique linéaire. L'application du résultat à l'identification qualittative d'une inclusion est présenté sur une configuration 2D acoustique simple.

This article is concerned with establishing the topological sensitivity (TS) against the nucleation of small trial inclusions of an energy-like cost function. The latter measures the discrepancy between two time-harmonic elastodynamic states (respectively defined, for cases where overdetermined boundary data is available for identification purposes, in terms of Dirichlet or Neumann boundary data for the same reference solid) as the strain energy of their difference. Such cost function constitutes a particular form of error in constitutive relation and may be used for e.g. defect identification. The TS is expressed in terms of four elastodynamic fields, namely the free and adjoint solutions for Dirichlet or Neumann data. A similar result is also given for the linear acoustic scalar case. A synthetic numerical example where the TS result is used for the qualitative identification of an inclusion is presented for a simple 2D acoustic configuration.

Publié le :
DOI : 10.1016/j.crme.2010.07.016
Keywords: Topological sensitivity, Energy-like functional, Elastodynamics, Defect identification
Mot clés : Gradient topologique, Fonction-coût énergétique, Elastodynamique, Identification de défauts
Marc Bonnet 1

1 Laboratoire de mécanique des solides (UMR CNRS 7649), École polytechnique, 91128 Palaiseau cedex, France 
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Marc Bonnet. Topological sensitivity of energy cost functional for wave-based defect identification. Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 377-389. doi : 10.1016/j.crme.2010.07.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.016/

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