Higher order topological derivatives for three-dimensional anisotropic elasticity

Marc Bonnet 1 Rémi Cornaggia 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This article concerns an extension of the topological derivative concept for 3D elasticity problems involving elastic inhomogeneities, whereby an objective function J is expanded in powers of the characteristic size a of a single small inhomogeneity. The O(a 6) approximation of J is derived and justified for an inhomogeneity of given location, shape and elastic properties embedded in a 3D solid of arbitrary shape and elastic properties; the background and the inhomogeneity materials may both be anisotropic. The generalization to multiple small inhomogeneities is concisely described. Computational issues, and examples of objective functions commonly used in solid mechanics, are discussed.
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Article dans une revue
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, pp.24. <10.1051/m2an/2017015>
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Contributeur : Marc Bonnet <>
Soumis le : vendredi 31 mars 2017 - 15:11:35
Dernière modification le : mercredi 12 avril 2017 - 17:02:34

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Marc Bonnet, Rémi Cornaggia. Higher order topological derivatives for three-dimensional anisotropic elasticity. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, pp.24. <10.1051/m2an/2017015>. <hal-01499498>

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