Free Access
Issue
ESAIM: M2AN
Volume 51, Number 6, November-December 2017
Page(s) 2069 - 2092
DOI https://doi.org/10.1051/m2an/2017015
Published online 27 November 2017
  1. 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 34 (2005)59–80. [Google Scholar]
  2. F. Alouges and M. Aussal, The sparse cardinal sine decomposition and its application for fast numerical convolution. Numer. Algorithms (2015) 1–22. [Google Scholar]
  3. H. Ammari, J. Garnier, V. Jugnon and H. Kang, Stability and resolution analysis for a topological derivative based imaging functional. SIAM J. Control Opt. 50 (2012) 48–76. [CrossRef] [Google Scholar]
  4. H. Ammari and H. Kang, Polarization and moment tensors: with applications to inverse problems and effective medium theory. Vol. 162. Springer (2007). [Google Scholar]
  5. 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. J. Elast. 67 (2002) 97–129. [Google Scholar]
  6. S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method. J. Comput. Phys. 216 (2006) 573–588. [Google Scholar]
  7. S. Andrieux and A. Ben Abda, The reciprocity gap: a general concept for flaws identification problems. Mech. Res. Commun. 20 (1993) 415–420. [Google Scholar]
  8. R.J. Asaro and D.M. Barnett, The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion. J. Mech. Phys. Solids 23 (1975) 77–83. [Google Scholar]
  9. C. Bellis and M. Bonnet, A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data. Int. J. Solids Struct. 47 (2010) 1221–1242. [Google Scholar]
  10. C. Bellis, M. Bonnet and F. Cakoni, Acoustic inverse scattering using topological derivative of far-field measurements-based cost functionals. Inverse Problems 29 (2013) 075012. [Google Scholar]
  11. M. Bonnet, Inverse acoustic scattering by small-obstacle expansion of a misfit function. Inverse Problems 24 (2008) 035022. [Google Scholar]
  12. M. Bonnet, Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems. “Special issue on the advances in mesh reduction methods - In honor of Professor Subrata Mukherjee on the occasion of his 65th birthday”. Eng. Anal. Boundary Elements 35 (2011) 223–235. [CrossRef] [Google Scholar]
  13. M. Bonnet and G. Delgado, The topological derivative in anisotropic elasticity. Quarterly J. Mech. Appl. Math. 66 (2013) 557–586. [CrossRef] [Google Scholar]
  14. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. 0172-5939. Springer Verlag New York (2011). [Google Scholar]
  15. P.G.Ciarlet, Linear and nonlinear functional analysis with applications. SIAM (2013). [Google Scholar]
  16. R. Dautray and J.L. Lions, Analyse mathematique et calcul numerique pour les sciences et les techniques. Masson (1984-85). [Google Scholar]
  17. J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. 241 (1957) 376–396. [Google Scholar]
  18. J. Eshelby, Elastic inclusions and inhomogeneities. Progress in solid Mechanics 2 (1961) 89–140. [Google Scholar]
  19. A.B. Freidin and V.A. Kucher, Solvability of the equivalent inclusion problem for an ellipsoidal inhomogeneity. Math. Mech. Solids 21 (2016) 255–262. [Google Scholar]
  20. Y. Fu, K.J. Klimkowski, G.J. Rodin, E. Berger, J.C. Browne, J.R. Singer, R.A. van der Greijn and K.S.Vemaganti, A fast solution method for the three-dimensional many-particle problems of linear elasticity. Int. J. Num. Meth. Eng. 42 (1998) 1215–1229. [CrossRef] [Google Scholar]
  21. S. Garreau, P. Guillaume and M. Masmoudi, The topological asymptotic for PDE systems: the elasticity case. SIAM J. Contr. Opt. 39 (2001) 1756–1778. [CrossRef] [MathSciNet] [Google Scholar]
  22. D. Gintides and K. Kiriaki, Solvability of the integrodifferential equation of Eshelby’s equivalent inclusion method. The Quarterly J. Mech. Appl. Math. 68 (2015) 85–96. [CrossRef] [Google Scholar]
  23. M. Grédiac and F. Hild, Full-field measurements and identification in solid mechanics. John Wiley and Sons (2012). [Google Scholar]
  24. G.C. Hsiaoa and W.L. Wendland, Boundary integral equations. Springer (2008). [Google Scholar]
  25. R. Kohn and A. McKenney, Numerical implementation of a variational method for electrical impedance tomography. Inverse Problems 6 (1990) 389–414. [Google Scholar]
  26. W.P. Kuykendall, W.D. Cash, D.M. Barnetta and W. Cai, On the existence of Eshelby’s equivalent ellipsoidal inclusion solution. Math. Mech. Solids 17 (2012) 840–847. [Google Scholar]
  27. P.A. Martin, Acoustic scattering by inhomogeneous obstacles. SIAM J. Appl. Math. 64 (2003) 297–308. [Google Scholar]
  28. M. Masmoudi, J. Pommier and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications. Inverse Problems 21 (2005) 547–564. [Google Scholar]
  29. W. McLean, Strongly elliptic systems and boundary integral equations. Cambridge (2000). [Google Scholar]
  30. S.G. Mikhlin and S. Prössdorf, Singular integral operators. Vol. 1986. Springer Verlag Berlin (1986). [Google Scholar]
  31. T. Mura, Micromechanics of defects in solids. M. Nijhoff, The Hague and Boston and Higham, Mass (1982). [Google Scholar]
  32. A.G. Ramm, A simple proof of the Fredholm alternative and a characterization of the Fredholm operators. Amer. Math. Monthly. 108 (2001) 855–860. [CrossRef] [Google Scholar]
  33. B. Samet, S. Amstutz and M. Masmoudi, The topological asymptotic for the Helmholtz equation. SIAM J. Contr. Opt. 42 (2004) 1523–1544. [CrossRef] [MathSciNet] [Google Scholar]
  34. M. Silva, M. Matalon and D.A. Tortorelli, Higher order topological derivatives in elasticity. Inter. J. Solids Structures 47 (2010) 3053–3066. [CrossRef] [Google Scholar]
  35. J. Sokolowski and A. Zochowski, Topological derivatives of shape functionals for elasticity systems. Mech. Based Design Struct. Machines 21 (2001) 331–349. [CrossRef] [EDP Sciences] [Google Scholar]
  36. T. Touhei, A fast volume integral equation method for elastic wave propagation in a half space. Int. J. Solids Struct. 48 (2011) 3194–3208. [Google Scholar]
  37. S. Xinchun and R.S. Lakes, Stability of elastic material with negative stiffness and negative Poisson’s ratio. Phys. Stat. Sol. 244 (2007) 1008–1026. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you