Free access
Issue
ESAIM: COCV
Volume 16, Number 3, July-September 2010
Page(s) 719 - 743
DOI http://dx.doi.org/10.1051/cocv/2009019
Published online 02 July 2009
  1. G. Allaire, Shape optimization by the homogenization method, Applied Mathematical Sciences 146. Springer-Verlag, New York (2002).
  2. G. Allaire, F. Jouve and N. Van Goethem, A level set method for the numerical simulation of damage evolution. Internal report 629, CMAP, École polytechnique, France (2007).
  3. H.D. Bui, Mécanique de la rupture fragile. Masson, Paris (1983).
  4. M. Burger, A framework for the construction of level set methods for shape optimization and reconstruction. Interface and Free Boundaries 5 (2003) 301–329. [CrossRef] [MathSciNet]
  5. B. Dacorogna, Direct methods in the calculus of variations, Applied Mathematical Sciences 78. Springer-Verlag, Berlin (1989).
  6. F. De Gournay, G. Allaire and F. Jouve, Shape and topology optimization of the robust compliance via the level set method. ESAIM: COCV 14 (2008) 43–70. [CrossRef] [EDP Sciences] [MathSciNet]
  7. P. Destuynder, Calculation of forward thrust of a crack, taking into account the unilateral contact between the lips of the crack. C. R. Acad. Sci. Paris, Sér. II 296 (1983) 745–748.
  8. P. Destuynder, An approach to crack propagation control in structural dynamics. C. R. Acad. Sci. Paris, Sér. II 306 (1988) 953–956.
  9. P. Destuynder, Remarks on a crack propagation control for stationary loaded structures. C. R. Acad. Sci. Paris, Sér. IIb 308 (1989) 697–701.
  10. P. Destuynder, Computation of an active control in fracture mechanics using finite elements. Eur. J. Mech. A/Solids 9 (1990) 133–141.
  11. P. Destuynder, M. Djaoua and S. Lescure, Quelques remarques sur la mécanique de la rupture élastique. J. Mec. Theor. Appl. 2 (1983) 113–135.
  12. M. Djaoua, Analyse mathématique et numérique de quelques problèmes en mécanique de la rupture. Thèse d'état, Université Paris VI, France (1983).
  13. G.A. Francfort and J.J. Marigo, Revisiting brittle fracture as an energy minimisation problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. [CrossRef] [MathSciNet]
  14. A.A. Griffith, The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. London 46 (1920) 163–198.
  15. P. Grisvard, Singularities in boundary value problems, Research in Applied Mathematics. Springer-Verlag, Berlin (1992).
  16. P. Hild, A. Münch and Y. Ousset, On the control of crack growth in elastic media. C. R. Acad. Sci. Paris Sér. Méc. 336 (2008) 422–427.
  17. P. Hild, A. Münch and Y. Ousset, On the active control of crack growth in elastic media. Comput. Methods Appl. Mech. Engrg. 198 (2008) 407–419. [CrossRef] [MathSciNet]
  18. J.-B. Leblond, Mécanique de la rupture fragile et ductile. Hermes Sciences Publications (2003) 1–197.
  19. K.L. Lurie, An introduction to the mathematical theory of dynamic materials, Advances in Mechanics and Mathematics 15. Springer (2007).
  20. F. Maestre, A. Münch and P. Pedregal, A spatio-temporal design problem for a damped wave equation. SIAM J. Appl Math. 68 (2007) 109–132. [CrossRef] [MathSciNet]
  21. A. Münch, Optimal design of the support of the control for the 2-D wave equation: numerical investigations. Int. J. Numer. Anal. Model. 5 (2008) 331–351. [MathSciNet]
  22. A. Münch and Y. Ousset, Energy release rate for a curvilinear beam. C. R. Acad. Sci. Paris, Sér. IIb 328 (2000) 471–476.
  23. A. Münch and Y. Ousset, Numerical simulation of delamination growth in curved interfaces. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2045–2067. [MathSciNet]
  24. A. Münch, P. Pedregal and F. Periago, Optimal design of the damping set for the stabilization of the wave equation. J. Diff. Eq. 231 (2006) 331–358. [CrossRef]
  25. A. Münch, P. Pedregal and F. Periago, Relaxation of an optimal design problem for the heat equation. J. Math. Pures Appl. 89 (2008) 225–247. [CrossRef] [MathSciNet]
  26. A. Münch, P. Pedregal and F. Periago, Optimal internal stabilization of the linear system of elasticity. Arch. Rational Mech. Analysis 193 (2009) 171–193. [CrossRef]
  27. F. Murat and J. Simon, Études de problèmes d'optimal design. Lect. Notes Comput. Sci. 41 (1976) 54–62.
  28. M.T. Niane, G. Bayili, A. Sène and M. Sy, Is it possible to cancel singularities in a domain with corners and cracks? C. R. Acad. Sci. Paris, Sér. I 343 (2006) 115–118.
  29. O. Pantz and K. Trabelsi, A post-treatment of the homogenization for shape optimization. SIAM J. Control. Optim. 47 (2008) 1380–1398. [CrossRef] [MathSciNet]
  30. P. Pedregal, Parametrized measures and variational principles. Birkhäuser (1997).
  31. P. Pedregal, Vector variational problems and applications to optimal design. ESAIM: COCV 11 (2005) 357–381. [CrossRef] [EDP Sciences]
  32. P. Pedregal, Optimal design in two-dimensional conductivity for a general cost depending on the field. Arch. Rational Mech. Anal. 182 (2006) 367–385. [CrossRef]
  33. P. Pedregal, Div-Curl Young measures and optimal design in any dimension. Rev. Mat. Comp. 20 (2007) 239–255.
  34. L. Tartar, An introduction to the Homogenization method in optimal design, in Lecture Notes in Mathematics 1740, A. Cellina and A. Ornelas Eds., Springer, Berlin/Heidelberg (2000) 47–156.