Open Access
Issue
ESAIM: COCV
Volume 25, 2019
Article Number 34
Number of page(s) 12
DOI https://doi.org/10.1051/cocv/2018021
Published online 13 September 2019
  1. L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Ration. Mech. Anal. 139 (1997) 201–238. [Google Scholar]
  2. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (2000). [Google Scholar]
  3. G. Anzellotti and M. Giaquinta, Existence of the displacement field for an elastoplastic body subject to Hencky’s law and von Mises yield condition. Manuscr. Math. 32 (1980) 101–136. [Google Scholar]
  4. G. Bellettini, A. Coscia and G. Dal Maso, Compactness and lower semicontinuity properties in SBD(Ω). Math. Z. 228 (1998) 337–351. [Google Scholar]
  5. B. Bourdin, G.A. Francfort and J.-J. Marigo, The variational approach to fracture. J. Elast. 91 (2008) 5–148. [Google Scholar]
  6. A. Braides and V. Chiadó Piat, Integral representation results for functionals defined on SBV(Ω; Rm). J. Math. Pures Appl. (9) 75 (1996) 595–626. [Google Scholar]
  7. A. Braides, S. Conti and A. Garroni, Density of polyhedral partitions. Calc. Var. Part. Differ. Equ. 56 (2017) 28. [Google Scholar]
  8. A. Chambolle, A density result in two-dimensional linearized elasticity, and applications. Arch. Ration. Mech. Anal. 167 (2003) 211–233. [Google Scholar]
  9. A. Chambolle, An approximation result for special functions with bounded deformation. J. Math. Pures Appl. 83 (2004) 929–954. [Google Scholar]
  10. A. Chambolle, Addendum to: “An approximation result for special functions with bounded deformation” [J. Math. Pures Appl. 83 (2004) 929–954]. J. Math. Pures Appl. 84 (2005) 137–145. [Google Scholar]
  11. A. Chambolle and V. Crismale, A Density Result in GSBDp with Applications to the Approximation of Brittle Fracture Energies. Arch. Ration. Mech. Anal. 232 (2019) 1329–1378. [Google Scholar]
  12. A. Chambolle, S. Conti and G. Francfort, Korn-Poincaré inequalities for functions with a small jump set. Indiana Univ. Math. J. 65 (2016) 1373–1399. [Google Scholar]
  13. A. Chambolle, S. Conti and G. Francfort, Approximation of a brittle fracture energy with a constraint of non-interpenetration. Arch. Ration. Mech. Anal. 228 (2018) 867–889. [Google Scholar]
  14. S. Conti, M. Focardi and F. Iurlano, Existence of minimizers for the 2d stationary Griffith fracture model. C. R. Acad. Sci. Paris Ser. I 354 (2016) 1055–1059. [Google Scholar]
  15. S. Conti, M. Focardi and F. Iurlano, Existence of Strong Minimizers for the Griffith Static Fracture Model in Dimension Two. Preprint arXiv:1611.03374 (2016). [Google Scholar]
  16. S. Conti, M. Focardi and F. Iurlano, Integral representation for functionals defined on SBDp in dimension two. Arch. Ration. Mech. Anal. 223 (2017) 1337–1374. [Google Scholar]
  17. S. Conti, M. Focardi and F. Iurlano, A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems. Preprint arXiv:1804.09945 (2018). [Google Scholar]
  18. G. Cortesani, Strong approximation of GSBV functions by piecewise smooth functions. Ann. Univ. Ferrara Sez. VII (N.S.) 43 (1997) 27–49 (1998). [Google Scholar]
  19. G. Cortesani and R. Toader, A density result in SBV with respect to non-isotropic energies. Nonlinear Anal. 38 (1999) 585–604. [Google Scholar]
  20. G. Dal Maso, Generalised functions of bounded deformation. J. Eur. Math. Soc. (JEMS) 15 (2013) 1943–1997. [Google Scholar]
  21. E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Ration. Mech. Anal. 108 (1989) 195–218. [Google Scholar]
  22. G.A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. [Google Scholar]
  23. M. Friedrich, A Korn-Poincaré-type Inequality for Special Functions of Bounded Deformation. Preprint arXiv:1503.06755 (2015). [Google Scholar]
  24. M. Friedrich, A Korn-type Inequality in SBD for Functions with Small Jump Sets. Preprint arXiv:1505.00565 (2015). [Google Scholar]
  25. J.W. Hutchinson, A Course on Nonlinear Fracture Mechanics. Department of Solid Mechanics, Techn. University of Denmark (1989). [Google Scholar]
  26. F. Iurlano, A density result for GSBD and its application to the approximation of brittle fracture energies. Calc. Var. Partial Differ. Equ. 51 (2014) 315–342. [Google Scholar]
  27. R. Kohn and R. Temam, Dual spaces of stresses and strains, with applications to Hencky plasticity. Appl. Math. Optim. 10 (1983) 1–35. [Google Scholar]
  28. P.-M. Suquet, Sur un nouveau cadre fonctionnel pour les équations de la plasticité. C. R. Acad. Sci. Paris Sér. A-B 286 (1978) A1129–A1132. [Google Scholar]
  29. R. Temam, Problèmes mathématiques en plasticité. Vol. 12 of Méthodes Mathématiques de l’Informatique. Gauthier-Villars, Montrouge (1983). [Google Scholar]
  30. R. Temam and G. Strang, Functions of bounded deformation. Arch. Ration. Mech. Anal. 75 (1980) 7–21. [Google Scholar]

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