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Dal Maso, Gianni and Giacomini, Alessandro and Ponsiglione, Marcello:
A Variational Model for Quasistatic Crack Growth in Nonlinear Elasticity: Some Qualitative Properties of the Solutions
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.2, p. 371-390, (English)
pdf (315 Kb), djvu (200 Kb). | MR 2537276 | Zbl 1173.74037

Sunto

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.
Referenze Bibliografiche
[1] L. AMBROSIO - N. FUSCO - D. PALLARA, Functions of bounded variations and free discontinuity problems. Clarendon Press, Oxford, 2000. | MR 1857292 | Zbl 0957.49001
[2] H. BREZIS, Convergence in $\mathcal{D}^{\prime}$ and in $L^{1}$ under strict convexity. Boundary value problems for partial differential equations and applications, 43-52, RMA Res. Notes Appl. Math., 29, Masson, Paris, 1993. | MR 1260437 | Zbl 0813.49016
[3] C. CASTAING - M. VALADIER, Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, Vol. 580, Springer-Verlag, Berlin-New York, 1977. | MR 467310 | Zbl 0346.46038
[4] A. CHAMBOLLE, A density result in two-dimensional linearized elasticity and applications. Arch. Ration. Mech. Anal., 167 (2003), 211-233. | fulltext (doi) | MR 1978582 | Zbl 1030.74007
[5] A. CHAMBOLLE - A. GIACOMINI - M. PONSIGLIONE, Crack initiation in brittle materials. Arch. Ration. Mech. Anal., 188 (2008), 309-349. | fulltext (doi) | MR 2385744 | Zbl 1138.74042
[6] B. DACOROGNA, Direct methods in the calculus of variations, Springer-Verlag, Berlin, 1989. | fulltext (doi) | MR 990890 | Zbl 0703.49001
[7] G. DAL MASO - G. A. FRANCFORT - R. TOADER, Quasi-static crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal., 176 (2005), 165-225. | fulltext (doi) | MR 2186036 | Zbl 1064.74150
[8] G. DAL MASO - R. TOADER, A model for the quasistatic growth of brittle fractures: existence and approximation results. Arch. Ration. Mech. Anal., 162 (2002), 101-135. | fulltext (doi) | MR 1897378 | Zbl 1042.74002
[9] E. DE GIORGI - L. AMBROSIO, Un nuovo tipo di funzionale del calcolo delle variazioni. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 82 (1988), 199-210. | fulltext EuDML | MR 1152641
[10] G. A. FRANCFORT - C. J. LARSEN, Existence and convergence for quasistatic evolution in brittle fracture. Comm. Pure Appl. Math., 56 (2003), 1465-1500. | fulltext (doi) | MR 1988896 | Zbl 1068.74056
[11] G. A. FRANCFORT - J.-J. MARIGO, Revisiting brittle fractures as an energy minimization problem. J. Mech. Phys. Solids, 46 (1998), 1319-1342. | fulltext (doi) | MR 1633984 | Zbl 0966.74060
[12] A. GRIFFITH, The phenomena of rupture and flow in solids. Philos. Trans. Roy. Soc. London Ser. A, 221 (1920), 163-198.
[13] A. MAINIK, Existence results for rate-independent phase transformations in shape-memory alloys. Arch. Ration. Mech. Anal., to appear.
[14] A. MIELKE, Evolution of rate-independent systems. In: Evolutionary equations. Vol. II. Edited by C.M. Dafermos and E. Feireisl, 461-559, Handbook of Differential Equations. Elsevier/North-Holland, Amsterdam, 2005. | MR 2182832 | Zbl 1120.47062
[15] R. T. ROCKAFELLAR, Convex analysis. Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J. 1970. | MR 274683
[16] K. YOSIDA, Functional analysis. Springer, 1965. | MR 180824

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