Geodesic
An Artificial Viscosity Approach to Quasistatic Crack Growth
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 1-35.

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We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$-gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero. 
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Toader, Rodica; Zanini, Chiara. An Artificial Viscosity Approach to Quasistatic Crack Growth. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 1-35. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_1_a0/

[1] J. Casado-Diaz - G. Dal Maso, A simplified model for the evolution of a fracture in a membrane, Preprint (2000). | Zbl

[2] A. Chambolle, A density result in two-dimensional linearized elasticity, and applications. Arch. Rational Mech. Anal., 167 (2003), 211-233. | DOI | MR | Zbl

[3] G. Dal Maso, G.A. Francfort AND R. Toader, Quasistatic Crack Growth in Nonlinear Elasticity, Arch. Rational Mech. Anal., 176 (2005), 165-225. | DOI | MR | Zbl

[4] 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. | DOI | MR | Zbl

[5] G. Dal Maso - R. Toader, A model for the quasi-static growth of brittle fractures based on local minimization, Math. Models Methods Appl. Sci., 12 (2002), 1773-1799. | DOI | MR | Zbl

[6] K. Deimling, Ordinary Differential Equations in Banach Spaces. Lect. Notes Math. 596, Springer-Verlag, Berlin-New York, 1977. | MR | Zbl

[7] G.A. Francfort - C.J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure Appl. Math., 56 (2003), 1465-1500. | DOI | MR | Zbl

[8] G. A. Francfort - J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46 (1998), 1319-1342. | DOI | MR | Zbl

[9] A. Friedman - B. Hu - J. J. L. Velazquez, The evolution of stress intensity factors in the propagation of two dimensional cracks, European J. Appl. Math., 11 (2000), 453-471. | DOI | MR | Zbl

[10] A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philos. Trans. R. Soc. London Ser. A, 221 (1920), 163-198.

[11] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24. Pitman (Advanced Publishing Program), Boston, MA, 1985. | MR | Zbl

[12] P. Grisvard, Singularities in Boundary Value Problems, Recherches en Mathématiques Appliquées [Research in Applied Mathematics], 22. Masson, Paris; Springer-Verlag, Berlin, 1992. | MR

[13] J. Hale, Ordinary Differential Equations, Pure and Applied Mathematics, XXI, Krieger, Florida, 1980. | MR

[14] D. Knees - A. Mielke, Energy release rate for cracks in finite-strain elasticity. Math. Methods Applied Sciences, 31 (2008), 501-528. | DOI | MR | Zbl

[15] S. G. Krantz - H. R. Parks, The Implicit Function Theorem. History, theory and applications. Birkhäuser, Boston, 2002. | DOI | MR | Zbl

[16] A. Mielke, Evolution of Rate-Independent Systems, Handbook of Differential Equations, Evolutionary Equations, v. 2, C.M. Dafermos, E. Feireisl (eds.) 461-559 Elsevier, Amsterdam, 2005. | MR | Zbl

[17] C. Zanini, Variational Techniques for Quasistatic Evolutionary Models, PhD Thesis, 2006, see http://digitallibrary.sissa.it/handle/1963/1874