Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurementsReportar como inadecuado

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1 APAM - Department of Applied Physics and Applied Mathematics 2 M&S - Matériaux et Structures LMA - Laboratoire de Mécanique et d-Acoustique Marseille 3 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France 4 Department of Mathematics University of Washington

Abstract : Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach.

Keywords : Quantitative parameter identification Internal data Regularization method Elastography Lamé system

Autor: Guillaume Bal - Cédric Bellis - Sébastien Imperiale - François Monard -



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