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A class of optimal virtual fields for inverse problems in elasticity
[Une classe de champs virtuels optimaux pour les problèmes inverses en élasticité]
Nagham Chibli1, 2, 3 orcid ; Martin Genet1 orcid ; Sébastien Imperiale2, 3 orcid 
1LMS, École Polytechnique, IPP – CNRS, France
2Inria, Inria-Saclay Île de France, France
3CMAP, École Polytechnique, IPP – CNRS, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 417-449

This work addresses the identification of nonhomogeneous constitutive parameters from full-field measurements in both linear and nonlinear elasticity, considering incompressible as well as compressible materials. The inverse identification procedure relies on the Virtual Fields Method (VFM), which is based on the principle of virtual work with specifically chosen virtual fields. We propose an optimal class of virtual fields, designed to optimize the reconstruction stability with respect to measurement noise. A series of numerical experiments illustrate the effectiveness of the proposed approach. The method exhibits moderate sensitivity to measurement noise and remains robust even when the boundary conditions are only partially known.

Ce travail porte sur l’identification de paramètres constitutifs hétérogènes à partir de mesures de champs internes, en élasticité linéaire et non linéaire, en considérant des matériaux incompressibles ainsi que compressibles. La procédure d’identification inverse repose sur la méthode des champs virtuels (VFM), fondée sur le principe des travaux virtuels avec des champs virtuels spécifiquement choisis. Nous proposons une classe optimale de champs virtuels, conçue pour optimiser la stabilité de la reconstruction vis-à-vis du bruit de mesure. Une série d’expériences numériques illustre l’efficacité de l’approche proposée. La méthode présente une sensibilité modérée au bruit de mesure et demeure robuste même lorsque les conditions aux limites ne sont que partiellement connues.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/crmeca.361
Keywords: Parameter identification, virtual fields method, elasticity, inverse problem
Mots-clés : Identification de paramètres, méthode des champs virtuels, élasticité, problème inverse

Nagham Chibli  1 , 2 , 3   ; Martin Genet  1   ; Sébastien Imperiale  2 , 3

1 LMS, École Polytechnique, IPP – CNRS, France
2 Inria, Inria-Saclay Île de France, France
3 CMAP, École Polytechnique, IPP – CNRS, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Nagham Chibli; Martin Genet; Sébastien Imperiale. A class of optimal virtual fields for inverse problems in elasticity. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 417-449. doi: 10.5802/crmeca.361
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     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {354},
     doi = {10.5802/crmeca.361},
     language = {en},
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