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A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only

Abstract : The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic parameters is possible, even for discontinuous parameters and without boundary information. We provide a general approach based on the weak definition of the stiffness-to-force operator which conduces to see the problem as a linear system. We prove that in the case of shear modulus reconstruction, we have an L 2-stability with only one measurement under minimal smoothness assumptions. This stability result is obtained though the proof that the linear operator to invert has closed range. We then describe a direct discretization which provides stable reconstructions of both isotropic and anisotropic stiffness tensors.
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https://hal.archives-ouvertes.fr/hal-02158452
Contributor : Laurent Seppecher Connect in order to contact the contributor
Submitted on : Tuesday, June 18, 2019 - 9:46:34 AM
Last modification on : Thursday, October 27, 2022 - 3:58:19 AM

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Habib Ammari, Elie Bretin, Pierre Millien, Laurent Seppecher. A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only. Numerische Mathematik, 2021, 147 (1), pp.189-226. ⟨10.1007/s00211-020-01164-6⟩. ⟨hal-02158452⟩

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