Un résumé de la théorie variationnelle de la rupture
- [1] Institut LAGA, Université Paris-Nord & Institut Universitaire de France 99, avenue Jean-Baptiste Clément 93430 Villetaneuse France
Séminaire Laurent Schwartz — EDP et applications (2011-2012)
- page 1-11
- ISSN: 2266-0607
Access Full Article
topHow to cite
topFrancfort, Gilles A.. "Un résumé de la théorie variationnelle de la rupture." Séminaire Laurent Schwartz — EDP et applications (2011-2012): 1-11. <http://eudml.org/doc/251157>.
@article{Francfort2011-2012,
affiliation = {Institut LAGA, Université Paris-Nord & Institut Universitaire de France 99, avenue Jean-Baptiste Clément 93430 Villetaneuse France},
author = {Francfort, Gilles A.},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {fre},
pages = {1-11},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Un résumé de la théorie variationnelle de la rupture},
url = {http://eudml.org/doc/251157},
year = {2011-2012},
}
TY - JOUR
AU - Francfort, Gilles A.
TI - Un résumé de la théorie variationnelle de la rupture
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 11
LA - fre
UR - http://eudml.org/doc/251157
ER -
References
top- L. Ambrosio, N. Fusco & D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, Oxford (2000). Zbl0957.49001MR1857292
- L. Ambrosio & V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via -convergence, Comm. Pure Appl. Math. 43 (1990), 999-1036. Zbl0722.49020MR1075076
- M. Amestoy & J.-B. Leblond, Crack paths in plane situation – II, Detailed form of the expansion of the stress intensity factors, Int. J. Solids Stuct. 29 (1989), 465–501. Zbl0755.73072MR1138337
- H.-A. Bahr, H.-J. Weiss, H.G. Maschke & F. Meissner, Multiple crack propagation in a strip caused by thermal shock, Theoretical and Applied Fracture Mechanics 10 (1988), 219–226.
- G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, dans : Adv. Appl. Mech., Vol. 7, Academic Press, New York (1962), 55–129. MR149728
- B. Bourdin, G. A. Francfort & J.-J. Marigo, The Variational Approach to Fracture, Springer, New York (2008). Zbl1176.74018MR2473620
- D. Bucur & N. Varchon, Boundary variation for a Neumann problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000), 807–821. Zbl1072.35063MR1822408
- A. Braides, G. Dal Maso & A. Garroni, Variational formulation of softening phenomena in fracture mechanics : the one dimensional case, Arch. Rat. Mech. Anal. 146 (1999), 23–58. Zbl0945.74006MR1682660
- A. Chambolle, A density result in two-dimensional linearized elasticity, and applications, Arch. Rational Mech. Anal. 167 (2003), 211–233. Zbl1030.74007MR1978582
- A. Chambolle, An approximation result for special functions with bounded variations, J. Math Pures Appl. 83 (2004), 929–954. Zbl1084.49038MR2074682
- A. Chambolle & F. Doveri, Continuity of Neumann linear elliptic problems on varying two-dimensional bounded open sets, Comm. Partial Differential Equations 22 (1997), 811–840. Zbl0901.35019MR1452169
- A. Chambolle, G. A. Francfort & J.-J. Marigo, Revisiting Energy Release Rates in Brittle Fracture, J. Nonlinear Sci. 20 (2010), 395–424. Zbl1211.74183MR2665275
- G. Dal Maso, G. A. Francfort & R. Toader, Quasistatic crack growth in nonlinear elasticity, Arch. Rational Mech. Anal. 176 (2005), 165–225. Zbl1064.74150MR2186036
- G. Dal Maso & G. Lazzaroni, Quasistatic crack growth in finite elasticity with non-interpenetration, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 257–290. Zbl1188.35205MR2580510
- G. Dal Maso & R. Toader, A Model for the Quasi-Static Growth of Brittle Fractures : Existence and Approximation Results, Arch. Rational Mech. Anal. 162 (2002), 101–135. Zbl1042.74002MR1897378
- G. A. Francfort & C. J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture, Commun. Pur. Appl. Math. 56 (2003), 1465–1500. Zbl1068.74056MR1988896
- G. A. Francfort & J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46 (1998), 1319–1342. Zbl0966.74060MR1633984
- A.A. Griffith, The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc. London CCXXI-A (1921), 163–198.
- A. Mielke, Evolution of rate-independent systems, dans : Evolutionary equations. Vol. II, Dafermos, A. and Feireisl, E., eds., Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam (2005), 41–559. Zbl1120.47062MR2182832
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.