Models for Dynamic Fracture Based on Griffith’s Criterion

Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 21)

Abstract

There has been much recent progress in extending Griffith’s criterion for crack growth into mathematical models for quasi-static crack evolution that are well-posed, in the sense that there exist solutions that can be numerically approximated. However, mathematical progress toward dynamic fracture (crack growth consistent with Griffith’s criterion, together with elastodynamics) has been more meager. We describe some recent results on a phase-field model of dynamic fracture, and introduce models for “sharp interface” dynamic fracture.

Keywords

Elastic Energy Dynamic Fracture Evolution Problem Maximal Dissipation Crack Increment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ambrosio, L. and Tortorelli, V.M.: On the approximation of free discontinuity problems, Boll. Un. Mat. Ital 6-B, 1992, 105–123.MathSciNetGoogle Scholar
  2. 2.
    Bourdin, B.: Numerical implementation of the variational formulation of brittle fracture, Interfaces Free Bound 9, 2007, 411–430.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bourdin, B., Larsen, C.J. and Richardson, C.L.: A time-discrete model for dynamic fracture based on crack regularization, submitted.Google Scholar
  4. 4.
    Chambolle, A.: A density result in two-dimensional linearized elasticity, and applications, Arch. Ration. Mech. Anal 167, 2003, 211–233.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Dal Maso, G., Francfort, G.A. and Toader, R.: Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal 176, 2005, 165–225.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dal Maso, G. and Toader, R.: A model for the quasi-static growth of brittle fractures: existence and approximation results, Arch. Ration. Mech. Anal 162, 2002, 101–135.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Francfort, F. and Marigo, J.-J.: Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46(8), 1998, 1319–1342.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Francfort, G.A. and Larsen, C.J.: Existence and convergence for quasi-static evolution in brittle fracture, Comm. Pure Appl. Math 56, 2003, 1465–1500.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Griffith, A.: The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc. London CCXXI-A, 1920, 163–198.Google Scholar
  10. 10.
    Giacomini, A.: Ambrosio–Tortorelli approximation of quasi-static evolution of brittle cracks, Calc. Variat. PDE 22, 2005, 129–172.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Larsen, C.J., Ortner, C. and Süli, E.: Existence of solutions to a regularized model of dynamic fracture, Mathematical Models and Methods in Applied Sciences, to appear.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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