Crack identification by 3D time-domain elastic or acoustic topological sensitivity

Cédric Bellis; Marc Bonnet

doi:10.1016/j.crme.2009.03.015

Crack identification by 3D time-domain elastic or acoustic topological sensitivity
[Identification de fissures par sensibilité topologique dynamique en élasticité ou acoustique tridimensionnelle]

Présenté par : Jean-Baptiste Leblond

Cédric Bellis ¹ ; Marc Bonnet ¹

¹ LMS, CNRS UMR 7649, École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 124-130.

Résumé
Abstract

L'analyse de sensibilité topologique, reposant sur le comportement asymptotique d'une fonction coût associée à la création d'un défaut virtuel infinitésimal dans un solide sain, fournit une méthode de calcul rapide et non itératif de construction d'une fonction indicatrice de défauts. Dans cette Note, consacrée à l'identification de fissures, le gradient topologique d'une fonctionnelle coût quelconque par rapport à l'apparition d'une fissure de taille infinitésimale est établi pour l'élastodynamique lineaire et l'acoustique. Les développements présentés reposent sur l'utilisation d'un état adjoint pour plus de simplicité et d'efficacité. Un exemple numérique en élastodynamique tridimensionnelle, basé sur une méthode d'éléments finis standard, valide l'intérêt de l'approche proposée.

The topological sensitivity analysis, based on the asymptotic behavior of a cost functional associated with the creation of a small trial flaw in a defect-free solid, provides a computationally-fast, non-iterative approach for identifying flaws embedded in solids. This concept is here considered for crack identification using time-dependent measurements on the external boundary. The topological derivative of a cost function under the nucleation of a crack of infinitesimal size is established, in the framework of time-domain elasticity or acoustics. The simplicity and efficiency of the proposed formulation is enhanced by the recourse to an adjoint solution. Numerical results obtained on a 3-D elastodynamic example using the conventional FEM demonstrate the usefulness of the topological derivative as a crack indicator function.

Reçu le : 2008-11-06
Accepté le : 2009-03-27
Publié le : 2009-03-01

DOI : 10.1016/j.crme.2009.03.015

Keywords: Computational solid mechanics, Topological sensitivity, Elastodynamics, Crack identification, Adjoint solution
Mots-clés : Mécanique des solides numérique, Sensibilité topologique, Elastodynamique, Identification de fissure, Etat adjoint

Affiliations des auteurs :

Cédric Bellis ¹ ; Marc Bonnet ¹

¹ LMS, CNRS UMR 7649, École polytechnique, 91128 Palaiseau cedex, France

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Cédric Bellis; Marc Bonnet. Crack identification by 3D time-domain elastic or acoustic topological sensitivity. Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 124-130. doi : 10.1016/j.crme.2009.03.015. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.03.015/

Bibliographie
Cité par

[1] M. Bonnet Topological sensitivity for 3D elastodynamics and acoustic inverse scattering in the time domain, Comput. Methods Appl. Mech. Engrg., Volume 195 (2006), pp. 5239-5254

[2] N. Dominguez; V. Gibiat; Y. Esquerré Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection, Wave Motion, Volume 42 (2005), pp. 31-52

[3] R. Gallego; G. Rus Identification of cracks and cavities using the topological sensitivity boundary integral equation, Comp. Mech., Volume 33 (2004), pp. 154-163

[4] H. Ammari; H. Kang Reconstruction of elastic inclusions of small volume via dynamic measurements, Appl. Math. Optim., Volume 54 (2006), pp. 223-235

[5] H. Ammari; H. Kang; H. Lee; W.K. Park Asymptotic imaging of perfectly conducting cracks, 2009 http://www.cmap.polytechnique.fr/~ammari/preprints (preprint)

[6] J.D. Achenbach Reciprocity in Elastodynamics, Cambridge University Press, 2003

[7] M. Bonnet Boundary Integral Equations Methods for Solids and Fluids, Wiley, 1999

[8] H. Ammari; L. Guadarrama Bustos; P. Garapon; H. Kang Transient anomaly imaging by the acoustic radiation force, 2009 http://www.cmap.polytechnique.fr/~ammari/preprints (preprint)

[9] H.D. Bui Mécanique de la rupture fragilel, Masson, 1978

[10] S. Amstutz; N. Dominguez Topological sensitivity analysis in the context of ultrasonic non-destructive testing, Eng. Anal. Boundary Elem., Volume 32 (2008), pp. 936-947

A. Makseev; T. V. Yakovleva; A. V. Krysko; M. V. Zhigalov; V. A. Krysko Identification of inclusions of arbitrary geometry with different physical properties of materials in 3D structures, International Journal of Mechanics and Materials in Design, Volume 21 (2025) no. 1, p. 53 | DOI:10.1007/s10999-024-09727-3
Evgeny Bazulin; Alexander Goncharsky; Sergey Romanov; Sergey Seryozhnikov Ultrasound transmission and reflection tomography for nondestructive testing using experimental data, Ultrasonics, Volume 124 (2022), p. 106765 | DOI:10.1016/j.ultras.2022.106765
E. G. Bazulin; A. V. Goncharskii; S. Yu. Romanov; S. Yu. Seryozhnikov Determining Geometric-Acoustic Properties of a Weld as a Solution to the Inverse Coefficient Problem for a Scalar Wave Equation, Russian Journal of Nondestructive Testing, Volume 57 (2021) no. 11, p. 933 | DOI:10.1134/s1061830921110036
E. G. Bazulin; A. V. Goncharsky; S. Yu. Romanov; S. Yu. Seryozhnikov Inverse Problems of Ultrasonic Tomography in Nondestructive Testing: Mathematical Methods and Experiment, Russian Journal of Nondestructive Testing, Volume 55 (2019) no. 6, p. 453 | DOI:10.1134/s1061830919060020
Eugene Bazulin; Alexander Goncharsky; Sergey Romanov Solving Inverse Problems of Ultrasound Tomography in a Nondestructive Testing on a Supercomputer, Supercomputing, Volume 1129 (2019), p. 392 | DOI:10.1007/978-3-030-36592-9_32
Kenta YOSHIHARA; Takahiko KURAHASHI; Yuki MURAKAMI; Shigehiro TOYAMA; Fujio IKEDA; Tetsuro IYAMA; Ikuo IHARA Estimation analysis of a defect depth in a concrete based on the adjoint variable method (Numerical experiment assuming observed displacement by the hammering test), Transactions of the JSME (in Japanese), Volume 85 (2019) no. 869, p. 18-00371 | DOI:10.1299/transjsme.18-00371
Fatemeh Pourahmadian; Bojan B. Guzina; Houssem Haddar A synoptic approach to the seismic sensing of heterogeneous fractures: From geometric reconstruction to interfacial characterization, Computer Methods in Applied Mechanics and Engineering, Volume 324 (2017), p. 395 | DOI:10.1016/j.cma.2017.06.002
Junya HATTORI; Hitoshi YOSHIKAWA DETERMINATION OF VARIOUS TYPES OF CRACKS IN A 2-D SCALAR WAVE FIELD USING TOPOLOGICAL DERIVATIVE, Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)), Volume 73 (2017) no. 2, p. I_255 | DOI:10.2208/jscejam.73.i_255
Jose Nadal-Serrano; Marisa Lopez-Vallejo A survey on theoretical and practical aspects of imaging aids for artificial vision in professional environments, IEEE Sensors Journal (2015), p. 1 | DOI:10.1109/jsen.2015.2390921
Fatemeh Pourahmadian; Bojan B. Guzina On the elastic-wave imaging and characterization of fractures with specific stiffness, International Journal of Solids and Structures, Volume 71 (2015), p. 126 | DOI:10.1016/j.ijsolstr.2015.06.014
Marc Bonnet Introduction to Identification Methods, Full‐Field Measurements and Identification in Solid Mechanics (2013), p. 223 | DOI:10.1002/9781118578469.ch8
Cédric Bellis; Marc Bonnet A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data, International Journal of Solids and Structures, Volume 47 (2010) no. 9, p. 1221 | DOI:10.1016/j.ijsolstr.2010.01.011
A.M. Khludnev; V.A. Kovtunenko; A. Tani On the topological derivative due to kink of a crack with non-penetration. Anti-plane model, Journal de Mathématiques Pures et Appliquées, Volume 94 (2010) no. 6, p. 571 | DOI:10.1016/j.matpur.2010.06.002

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