M. A. Aguilo, W. Aquino, J. C. Brigham, and M. Fatemi, An Inverse Problem Approach for Elasticity Imaging through Vibroacoustics, IEEE Transactions on Medical Imaging, vol.29, issue.4, pp.1012-1021, 2010.
DOI : 10.1109/TMI.2009.2039225

U. Albocher, A. A. Oberai, P. E. Barbone, and I. Harari, Adjoint-weighted equation for inverse problems of incompressible plane-stress elasticity, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.30-32, pp.2412-2420, 2009.
DOI : 10.1016/j.cma.2009.02.034

O. Allix, P. Feissel, and H. M. Nguyen, Identification strategy in the presence of corrupted measurements, Engineering Computations, vol.22, issue.5/6, pp.487-504, 2005.
DOI : 10.1108/02644400510602989
URL : https://hal.archives-ouvertes.fr/hal-00022253

B. Banerjee, T. F. Walsh, W. Aquino, and M. Bonnet, Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional, Computer Methods in Applied Mechanics and Engineering, vol.253, pp.60-72, 2013.
DOI : 10.1016/j.cma.2012.08.023
URL : https://hal.archives-ouvertes.fr/hal-00732291

D. Barthe, P. Ladeveze, A. Deraemaeker, and S. L. Loch, Validation and Updating of Industrial Models Based on the Constitutive Relation Error, AIAA Journal, vol.42, issue.7, pp.1427-1434, 2004.
DOI : 10.2514/1.11882

M. Bonnet and A. Constantinescu, Inverse problems in elasticity, Inverse Problems, vol.21, issue.2, p.1, 2005.
DOI : 10.1088/0266-5611/21/2/R01
URL : https://hal.archives-ouvertes.fr/hal-00111264

J. Brigham, W. Aquino, F. Mitri, J. Greenleaf, and M. Fatemi, Inverse estimation of viscoelastic material properties for solids immersed in fluids using vibroacoustic techniques, Journal of Applied Physics, vol.101, issue.2, pp.23509-023509, 2007.
DOI : 10.1063/1.2423227

R. Christensen, Theory of Viscoelasticity, Journal of Applied Mechanics, vol.38, issue.3, 1982.
DOI : 10.1115/1.3408900

D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2012.

M. Doyley, P. Meaney, and J. Bamber, Evaluation of an iterative reconstruction method for quantitative elastography, Physics in Medicine and Biology, vol.45, issue.6, p.1521, 2000.
DOI : 10.1088/0031-9155/45/6/309

P. Feissel and O. Allix, Modified constitutive relation error identification strategy for transient dynamics with corrupted data: The elastic case. Computer methods in applied mechanics and engineering, pp.1968-1983, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00131857

Y. Fung, Biomechanics: mechanical properties of living tissues, 1981.

L. Gao, K. Parker, R. Lerner, and S. Levinson, Imaging of the elastic properties of tissue???A review, Ultrasound in Medicine & Biology, vol.22, issue.8, pp.959-977, 1996.
DOI : 10.1016/S0301-5629(96)00120-2

Z. Grasely, Measuring and modeling the time-dependent response of cementitious materials to internal stresses, 2006.

J. F. Greenleaf, M. Fatemi, and M. Insana, Selected Methods for Imaging Elastic Properties of Biological Tissues, Annual Review of Biomedical Engineering, vol.5, issue.1, pp.57-78, 2003.
DOI : 10.1146/annurev.bioeng.5.040202.121623

V. Isakov, Inverse problems for partial differential equations, 2006.

P. Ladevèze and D. Leguillon, Error Estimate Procedure in the Finite Element Method and Applications, SIAM Journal on Numerical Analysis, vol.20, issue.3, pp.485-509, 1983.
DOI : 10.1137/0720033

P. Ladevèze, D. Nedjar, and M. Reynier, Updating of finite element models using vibration tests, AIAA Journal, vol.32, issue.7, pp.1485-1491, 1994.
DOI : 10.2514/3.12219

J. Nocedal and S. J. Wright, Numerical Optimization 2nd, 2006.

A. A. Oberai, N. H. Gokhale, and G. R. Feijoo, Solution of inverse problems in elasticity imaging using the adjoint method, Inverse Problems, vol.19, issue.2, p.297, 2003.
DOI : 10.1088/0266-5611/19/2/304

T. E. Oliphant, A. Manduca, R. L. Ehman, and J. F. Greenleaf, Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation, Magnetic Resonance in Medicine, vol.1, issue.2, pp.299-310, 2001.
DOI : 10.1002/1522-2594(200102)45:2<299::AID-MRM1039>3.0.CO;2-O

J. Ophir, S. Alam, B. Garra, F. Kallel, E. Konofagou et al., Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues, Proceedings of the Institution of Mechanical Engineers, pp.203-233, 1999.
DOI : 10.1243/0954411991534933

E. Park and A. M. Maniatty, Shear modulus reconstruction in dynamic elastography: time harmonic case, Physics in Medicine and Biology, vol.51, issue.15, p.3697, 2006.
DOI : 10.1088/0031-9155/51/15/007

K. Parker, L. Gao, R. Lerner, and S. Levinson, Techniques for elastic imaging: a review, IEEE Engineering in Medicine and Biology Magazine, vol.15, issue.6, pp.52-59, 1996.
DOI : 10.1109/51.544512

K. J. Parker, L. S. Taylor, S. Gracewski, and D. J. Rubens, A unified view of imaging the elastic properties of tissue, The Journal of the Acoustical Society of America, vol.117, issue.5, p.2705, 2005.
DOI : 10.1121/1.1880772

O. Schenk and K. Gärtner, Solving unsymmetric sparse systems of linear equations with PARDISO, Future Generation Computer Systems, vol.20, issue.3, pp.475-487, 2004.
DOI : 10.1016/j.future.2003.07.011

O. Schenk and K. Gärtner, On fast factorization pivoting methods for sparse symmetric indefinite systems, Electronic Transactions on Numerical Analysis, vol.23, pp.158-179, 2006.

R. Sinkus, M. Tanter, S. Catheline, J. Lorenzen, C. Kuhl et al., Imaging anisotropic and viscous properties of breast tissue by magnetic resonance-elastography, Magnetic Resonance in Medicine, vol.8, issue.2, pp.372-387, 2005.
DOI : 10.1002/mrm.20355

J. E. Warner, M. I. Diaz, W. Aquino, and M. Bonnet, Inverse material identification in coupled acoustic-structure interaction using a modified error in constitutive equation functional, Computational Mechanics, vol.28, issue.10, pp.1-15, 2014.
DOI : 10.1007/s00466-014-1018-0
URL : https://hal.archives-ouvertes.fr/hal-00977526

Y. Zhang, A. A. Oberai, P. E. Barbone, and I. Harari, Solution of the time-harmonic viscoelastic inverse problem with interior data in two dimensions, International Journal for Numerical Methods in Engineering, vol.47, issue.6, pp.1100-1116, 2012.
DOI : 10.1002/nme.4372