A modified error in constitutive equation approach for frequency-domain viscoelasticity imaging using interior data

Manuel I. Diaz 1 Wilkins Aquino 1 Marc Bonnet 2
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This paper presents a methodology for the inverse identification of linearly viscoelastic material parameters in the context of steady-state dynamics using interior data. The inverse problem of viscoelasticity imaging is solved by minimizing a modified error in constitutive equation (MECE) functional, subject to the conservation of linear momentum. The treatment is applicable to configurations where boundary conditions may be partially or completely underspecified. The MECE functional measures the discrepancy in the consti-tutive equations that connect kinematically admissible strains and dynamically admissible stresses, and also incorporates the measurement data in a quadratic penalty term. Regularization of the problem is achieved through a penalty parameter in combination with the discrepancy principle due to Morozov. Numerical results demonstrate the robust performance of the method in situations where the available measurement data is incomplete and corrupted by noise of varying levels.
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Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 296, pp.129-149. 〈10.1016/j.cma.2015.07.025〉
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Manuel I. Diaz, Wilkins Aquino, Marc Bonnet. A modified error in constitutive equation approach for frequency-domain viscoelasticity imaging using interior data. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 296, pp.129-149. 〈10.1016/j.cma.2015.07.025〉. 〈hal-01183511〉

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