We present the main existence result for quasistatic crack growth in the model proposed by Dal Maso, Francfort, and Toader, and prove some qualitative properties of the solutions.
@article{BUMI_2009_9_2_2_371_0, author = {Gianni Dal Maso and Alessandro Giacomini and Marcello Ponsiglione}, title = {A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {2}, year = {2009}, pages = {371-390}, zbl = {1173.74037}, mrnumber = {2537276}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_2_371_0} }
Dal Maso, Gianni; Giacomini, Alessandro; Ponsiglione, Marcello. A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 371-390. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_2_371_0/
[1] | MR 1857292 | Zbl 0957.49001
- - , Functions of bounded variations and free discontinuity problems. Clarendon Press, Oxford, 2000.[2] 29, Masson, Paris, 1993. | MR 1260437 | Zbl 0813.49016
, Convergence in and in under strict convexity. Boundary value problems for partial differential equations and applications, 43-52, RMA Res. Notes Appl. Math.,[3] 580, Springer-Verlag, Berlin-New York, 1977. | MR 467310 | Zbl 0346.46038
- , Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, Vol.[4] A density result in two-dimensional linearized elasticity and applications.Arch. Ration. Mech. Anal., 167 (2003), 211-233. | MR 1978582 | Zbl 1030.74007
,[5] Crack initiation in brittle materials. Arch. Ration. Mech. Anal., 188 (2008), 309-349. | MR 2385744 | Zbl 1138.74042
- - ,[6] | MR 990890 | Zbl 0703.49001
, Direct methods in the calculus of variations, Springer-Verlag, Berlin, 1989.[7] Quasi-static crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal., 176 (2005), 165-225. | MR 2186036 | Zbl 1064.74150
- - ,[8] A model for the quasistatic growth of brittle fractures: existence and approximation results. Arch. Ration. Mech. Anal., 162 (2002), 101-135. | MR 1897378 | Zbl 1042.74002
- ,[9] Un nuovo tipo di funzionale del calcolo delle variazioni. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 82 (1988), 199-210. | MR 1152641
- ,[10] Existence and convergence for quasistatic evolution in brittle fracture. Comm. Pure Appl. Math., 56 (2003), 1465-1500. | MR 1988896 | Zbl 1068.74056
- ,[11] Revisiting brittle fractures as an energy minimization problem. J. Mech. Phys. Solids, 46 (1998), 1319-1342. | MR 1633984 | Zbl 0966.74060
- ,[12] The phenomena of rupture and flow in solids. Philos. Trans. Roy. Soc. London Ser. A, 221 (1920), 163-198.
,[13] Existence results for rate-independent phase transformations in shape-memory alloys. Arch. Ration. Mech. Anal., to appear.
,[14] Evolution of rate-independent systems. In: Evolutionary equations. Vol. II. Edited by and , 461-559, Handbook of Differential Equations. Elsevier/North-Holland, Amsterdam, 2005. | MR 2182832 | Zbl 1120.47062
,[15] 28, Princeton University Press, Princeton, N.J.1970. | MR 274683
, Convex analysis. Princeton Mathematical Series, No.[16] | MR 180824
, Functional analysis. Springer, 1965.