We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified -gradient flow of the energy functional, as the "viscosity" parameter tends to zero.
@article{BUMI_2009_9_2_1_1_0, author = {Rodica Toader and Chiara Zanini}, title = {An Artificial Viscosity Approach to Quasistatic Crack Growth}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {2}, year = {2009}, pages = {1-35}, zbl = {1180.35521}, mrnumber = {2493642}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_1_1_0} }
Toader, Rodica; Zanini, Chiara. An Artificial Viscosity Approach to Quasistatic Crack Growth. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 1-35. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_1_1_0/
[1] A simplified model for the evolution of a fracture in a membrane, Preprint (2000). | Zbl 0959.49014
- ,[2] A density result in two-dimensional linearized elasticity, and applications. Arch. Rational Mech. Anal., 167 (2003), 211-233. | MR 1978582 | Zbl 1030.74007
,[3] Quasistatic Crack Growth in Nonlinear Elasticity, Arch. Rational Mech. Anal., 176 (2005), 165-225. | MR 2186036 | Zbl 1064.74150
, AND ,[4] A model for the quasi-static growth of brittle fractures: existence and approximation results, Arch. Rational Mech. Anal., 162 (2002), 101-135. | MR 1897378 | Zbl 1042.74002
- ,[5] A model for the quasi-static growth of brittle fractures based on local minimization, Math. Models Methods Appl. Sci., 12 (2002), 1773-1799. | MR 1946723 | Zbl 1205.74149
- ,[6] 596, Springer-Verlag, Berlin-New York, 1977. | MR 463601 | Zbl 0361.34050
, Ordinary Differential Equations in Banach Spaces. Lect. Notes Math.[7] Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure Appl. Math., 56 (2003), 1465-1500. | MR 1988896 | Zbl 1068.74056
- ,[8] Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46 (1998), 1319-1342. | MR 1633984 | Zbl 0966.74060
- ,[9] The evolution of stress intensity factors in the propagation of two dimensional cracks, European J. Appl. Math., 11 (2000), 453-471. | MR 1799921 | Zbl 0969.74056
- - ,[10] The Phenomena of Rupture and Flow in Solids, Philos. Trans. R. Soc. London Ser. A, 221 (1920), 163-198.
,[11] 24. Pitman (Advanced Publishing Program), Boston, MA, 1985. | MR 775683 | Zbl 0695.35060
, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics,[12] 22. Masson, Paris; Springer-Verlag, Berlin, 1992. | MR 1173209
, Singularities in Boundary Value Problems, Recherches en Mathématiques Appliquées [Research in Applied Mathematics],[13] XXI, Krieger, Florida, 1980. | MR 587488
, Ordinary Differential Equations, Pure and Applied Mathematics,[14] Energy release rate for cracks in finite-strain elasticity. Math. Methods Applied Sciences, 31 (2008), 501-528. | MR 2394124 | Zbl 1132.74038
- ,[15] | MR 1894435 | Zbl 1012.58003
- , The Implicit Function Theorem. History, theory and applications. Birkhäuser, Boston, 2002.[16] Evolution of Rate-Independent Systems, Handbook of Differential Equations, Evolutionary Equations, v. 2, , (eds.) 461-559 Elsevier, Amsterdam, 2005. | MR 2549367 | Zbl 1120.47062
,[17] Variational Techniques for Quasistatic Evolutionary Models, PhD Thesis, 2006, see http://digitallibrary.sissa.it/handle/1963/1874
,