Open Access
Volume 25, 2019
Article Number 34
Number of page(s) 12
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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Dal Maso, Generalised functions of bounded deformation. J. Eur. Math. Soc. (JEMS) 15 (2013) 1943–1997. [CrossRef] [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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