G. Allaire, F. De-gournay, F. Jouve, and A. M. Toader, Structural optimization using topological and shape sensitivity via a level-set method, Control and Cybernetics, vol.34, pp.59-80, 2005.

F. Alouges and M. Aussal, The sparse cardinal sine decomposition and its application for fast numerical convolution, Numerical Algorithms, vol.98, issue.3, pp.1-22, 2015.
DOI : 10.1007/s11075-014-9953-6

H. Ammari, J. Garnier, V. Jugnon, and H. Kang, Stability and Resolution Analysis for a Topological Derivative Based Imaging Functional, SIAM Journal on Control and Optimization, vol.50, issue.1, pp.48-76, 2012.
DOI : 10.1137/100812501
URL : https://hal.archives-ouvertes.fr/hal-00695667

H. Ammari and H. Kang, Polarization and moment tensors: with applications to inverse problems and effective medium theory, 2007.

H. Ammari, H. Kang, G. Nakamura, and K. Tanuma, Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion, Journal of Elasticity, vol.67, issue.2, pp.97-129, 2002.
DOI : 10.1023/A:1023940025757

S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, vol.216, issue.2, pp.573-588, 2006.
DOI : 10.1016/j.jcp.2005.12.015

S. Andrieux, B. Abda, and A. , The reciprocity gap: a general concept for flaws identification problems, Mechanics Research Communications, vol.20, issue.5, pp.415-420, 1993.
DOI : 10.1016/0093-6413(93)90032-J

R. J. Asaro and D. M. Barnett, The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion, Journal of the Mechanics and Physics of Solids, vol.23, issue.1, pp.77-83, 1975.
DOI : 10.1016/0022-5096(75)90012-5

C. Bellis and M. Bonnet, A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data, International Journal of Solids and Structures, vol.47, issue.9, pp.1221-1242, 2010.
DOI : 10.1016/j.ijsolstr.2010.01.011
URL : https://hal.archives-ouvertes.fr/hal-00446550

C. Bellis, M. Bonnet, and F. Cakoni, cost functionals, Inverse Problems, vol.29, issue.7, p.75012, 2013.
DOI : 10.1088/0266-5611/29/7/075012
URL : https://hal.archives-ouvertes.fr/hal-01323305

M. Bonnet, Inverse acoustic scattering by small-obstacle expansion of a misfit function, Inverse Problems, vol.24, issue.3, p.35022, 2008.
DOI : 10.1088/0266-5611/24/3/035022

M. Bonnet, Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems. Engineering Analysis with Boundary Elements ¡ce:title¿Special issue on the advances in mesh reduction methods-In honor of Professor, pp.223-235, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00495407

M. Bonnet and G. Delgado, The topological derivative in anisotropic elasticity, The Quarterly Journal of Mechanics and Applied Mathematics, vol.66, issue.4, pp.557-586, 2013.
DOI : 10.1093/qjmam/hbt018
URL : https://hal.archives-ouvertes.fr/hal-00852248

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. 0172-5939, 2011.
DOI : 10.1007/978-0-387-70914-7

P. G. Ciarlet, Linear and nonlinear functional analysis with applications, SIAM, 2013.

R. Dautray and J. L. Lions, Analyse mathematique et calcul numerique pour les sciences et les techniques, 1984.

J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society, pp.376-396, 1957.

J. Eshelby, Elastic inclusions and inhomogeneities. Progress in solid mechanics, pp.89-140, 1961.
DOI : 10.1007/1-4020-4499-2_26

A. B. Freidin and V. A. Kucher, Solvability of the equivalent inclusion problem for an ellipsoidal inhomogeneity, Mathematics and Mechanics of Solids, vol.21, issue.2, pp.255-262, 2016.
DOI : 10.1177/1081286515588636

Y. Fu, K. J. Klimkowski, G. J. Rodin, E. Berger, J. C. Browne et al., A fast solution method for three-dimensional many-particle problems of linear elasticity, International Journal for Numerical Methods in Engineering, vol.71, issue.7, pp.1215-1229, 1998.
DOI : 10.1002/(SICI)1097-0207(19980815)42:7<1215::AID-NME406>3.0.CO;2-5

S. Garreau, P. Guillaume, and M. Masmoudi, The Topological Asymptotic for PDE Systems: The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001.
DOI : 10.1137/S0363012900369538

D. Gintides and K. Kiriaki, Solvability of the integrodifferential equation of Eshelby's equivalent inclusion method, The Quarterly Journal of Mechanics and Applied Mathematics, vol.68, issue.1, pp.85-96, 2015.
DOI : 10.1093/qjmam/hbu025

M. Grédiac and F. Hild, Full-field measurements and identification in solid mechanics, 2012.
DOI : 10.1002/9781118578469

G. C. Hsiao and W. L. Wendland, Boundary integral equations, 2008.

R. Kohn and A. Mckenney, Numerical implementation of a variational method for electrical impedance tomography, Inverse Problems, vol.6, issue.3, pp.389-414, 1990.
DOI : 10.1088/0266-5611/6/3/009

W. P. Kuykendall, W. D. Cash, D. M. Barnett, and W. Cai, On the existence of Eshelby's equivalent ellipsoidal inclusion solution, Mathematics and Mechanics of Solids, vol.17, issue.8, pp.840-847, 2012.
DOI : 10.1177/1081286511433082

P. A. Martin, Acoustic Scattering by Inhomogeneous Obstacles, SIAM Journal on Applied Mathematics, vol.64, issue.1, pp.297-308, 2003.
DOI : 10.1137/S0036139902414379

M. Masmoudi, J. Pommier, and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, vol.21, issue.2, pp.547-564, 2005.
DOI : 10.1088/0266-5611/21/2/008

W. Mclean, Strongly elliptic systems and boundary integral equations, Cambridge, 2000.

S. G. Mikhlin and S. Prössdorf, Singular integral operators, 1986.
DOI : 10.1007/978-3-642-61631-0

T. Mura, Micromechanics of defects in solids. M. Nijhoff (The Hague and Boston and Higham, Mass.), 1982.

A. G. Ramm, A Simple Proof of the Fredholm Alternative and a Characterization of the Fredholm Operators, The American Mathematical Monthly, vol.108, issue.9, pp.855-860, 2001.
DOI : 10.2307/2695558

B. Samet, S. Amstutz, and M. Masmoudi, The Topological Asymptotic for the Helmholtz Equation, SIAM Journal on Control and Optimization, vol.42, issue.5, pp.1523-1544, 2004.
DOI : 10.1137/S0363012902406801

M. Silva, M. Matalon, and D. A. Tortorelli, Higher order topological derivatives in elasticity, International Journal of Solids and Structures, vol.47, issue.22-23, pp.3053-3066, 2010.
DOI : 10.1016/j.ijsolstr.2010.07.004
URL : http://doi.org/10.1016/j.ijsolstr.2010.07.004

J. Sokolowski and A. Zochowski, Topological derivatives of shape functionals for elasticity systems. Mechanics Based Design of Structures and Machines, pp.331-349, 2001.

T. Touhei, A fast volume integral equation method for elastic wave propagation in a half space, International Journal of Solids and Structures, vol.48, issue.22-23, pp.3194-3208, 2011.
DOI : 10.1016/j.ijsolstr.2011.07.013

S. Xinchun and R. S. Lakes, Stability of elastic material with negative stiffness and negative Poisson's ratio, physica status solidi (b), vol.8, issue.3, pp.1008-1026, 2007.
DOI : 10.1002/pssb.200572719