Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Negri, Matteo; Ortner, Christoph (2008)
Publisher: World Scientific Publishing Co. Pte. Ltd.
Languages: English
Types: Article
Subjects: QA, TA
We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith's criterion in a suitable form which takes into account both stable and unstable propagations, as well as an energy balance formula which accounts for dissipation in the unstable regime. If the load is monotonically increasing, this solution is explicit and almost everywhere unique. For more general loads we construct a solution via time discretization. Finally, we consider a finite element discretization of the problem and prove convergence of the discrete solutions.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1. L. Ambrosio, N. Fusco, and D. Pallara. Functions of bounded variation and free discontinuity problems. Oxford University Press, New York, 2000.
    • 2. J. Banasiak and G. F. Roach. On mixed boundary value problems of Dirichlet obliquederivative type in plane domains with piecewise differentiable boundary. J. Differential Equations, 79(1):111-131, 1989.
    • 3. H. Blum and M. Dobrowolski. On finite element methods for elliptic equations on domains with corners. Computing, 28(1):53-63, 1982.
    • 4. B. Bourdin, G.A. Francfort, and J.J. Marigo. Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids, 48(4):797-826, 2000.
    • 5. S.C. Brenner and L.Y. Sung. Multigrid methods for the computation of singular solutions and stress intensity factors. II. Crack singularities. BIT, 37(3):623-643, 1997.
    • 6. Z. Cai, S. Kim, S. Kim, and S. Kong. A finite element method using singular functions for poisson equations: Mixed boundary conditions. Comput. Methods Appl. Mech. Engrg., 195:2635-2648, 2006.
    • 7. A. Chambolle. A density result in two-dimensional linearized elasticity and applications. Arch. Ration. Mech. Anal., 167(3):211-233, 2003.
    • 8. A. Chambolle, A. Giacomini, and M. Ponsiglione. Crack initiation in elastic bodies. Arch. Ration. Mech. Anal., to appear.
    • 9. P.G. Ciarlet. The finite element method for elliptic problems. Studies in Mathematics and its Applications, Vol. 4. North-Holland Publishing Co., Amsterdam, 1978.
    • 10. G. Dal Maso, G.A. Francfort, and R. Toader. Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal., 176(2):165-225, 2005.
    • 11. P. Destuynder and M. Djaoua. Sur une interpr´etation math´ematique de l'int´egrale de Rice en th´eorie de la rupture fragile. Math. Methods Appl. Sci., 3(1):70-87, 1981.
    • 12. M.A. Efendiev and A. Mielke. On the rate-independent limit of systems with dry friction and small viscosity. J. Convex Anal., 13(1):151-167, 2006.
    • 13. G.A. Francfort and C.J. Larsen. Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure Appl. Math., 56(10):1465-1500, 2003.
    • 14. G.A. Francfort and J.J. Marigo. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids, 46(8):1319-1342, 1998.
    • 15. A. Giacomini and M. Ponsiglione. A discontinuous finite element approximation of quasi-static growth of brittle fractures. Numer. Funct. Anal. Optim., 24(7-8):813-850, 2003.
    • 16. A.A. Griffith. The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. London, 18:16-98, 1920.
    • 17. P. Grisvard. Elliptic problems in nonsmooth domains. Pitman (Advanced Publishing Program), Boston, MA, 1985.
    • 18. P. Grisvard. Singularities in boundary value problems. Masson, Paris, 1992.
    • 19. D. Knees, A. Mielke, and C. Zanini. On the inviscid limit of a model for crack propagation. Math. Mod. Meth. Appl. Sci., 18(11), 2008.
    • 20. M. Koˇcvara, A. Mielke, and T. Roub´ıˇcek. A rate-independent approach to the delamination problem. Math. Mech. Solids, 11(4):423-447, 2006.
    • 21. G.A. Maugin. The thermomechanics of plasticity and fracture. Cambridge University Press, Cambridge, 1992.
    • 22. A. Mielke, R. Rossi, and G. Savar´e. A metric approach to a class of doubly-nonlinear evolution equations and applications. Technical Report 1226, WIAS, 2007.
    • 23. M. Negri. A finite element approximation of the Griffith's model in fracture mechanics. Numer. Math., 95(4):653-687, 2003.
    • 24. R. Toader and C. Zanini. An artificial viscosity approach to quasi-static crack growth. Technical Report 43/2006/M, SISSA, 2006.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article