Continuum Mechanics and Thermodynamics

, Volume 20, Issue 1, pp 1–19 | Cite as

Dynamic fracture: an example of convergence towards a discontinuous quasistatic solution

  • P.-E. Dumouchel
  • J.-J. MarigoEmail author
  • M. Charlotte
Original Article


Considering a one-dimensional problem of debonding of a thin film in the context of Griffith’s theory, we show that the dynamical solution converges, when the speed of loading goes down to 0, to a quasistatic solution including an unstable phase of propagation. In particular, the jump of the debonding induced by this instability is governed by a principle of conservation of the total quasistatic energy, the kinetic energy being negligible.


Fracture mechanics Shock waves Nonlinear stability 


62.20.Mk 62.50 43.25.Cb 68.35.Ja 83.60.Uv 


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  1. 1.
    Berry J. (1960). Some kinetic considerations of the Griffith criterion for fracture—I: Equations of motion at constant force. J. Mech. Phys. Solids 8(3): 194–206 CrossRefMathSciNetGoogle Scholar
  2. 2.
    Berry J. (1960). Some kinetic considerations of the Griffith criterion for fracture—II: Equations of motion at constant deformation. J. Mech. Phys. Solids 8(3): 207–216 CrossRefMathSciNetGoogle Scholar
  3. 3.
    Mielke, A.: Evolution of rate-independent systems. In: Evolutionary equations, vol. II of Handb. Differ. Equ., pp. 461–559. Elsevier/North-Holland, Amsterdam (2005)Google Scholar
  4. 4.
    Francfort G.A. and Mielke A. (2006). Existence results for a class of rate-independent material models with nonconvex elastic energies. J. Reine Angew. Math. 595: 55–91 MathSciNetzbMATHGoogle Scholar
  5. 5.
    Bourdin, B., Francfort, G.A., Marigo, J.-J.: The variational approach to fracture. J. Elast. (2008) (to appear)Google Scholar
  6. 6.
    Obreimoff J.W. (1930). The splitting strength of mica. Proc. R. Soc. Lond. A 127: 290–297 CrossRefGoogle Scholar
  7. 7.
    Lawn B. (1993). Fracture of Brittle Solids, 2nd edn, Cambridge Solid State Science Series. Cambridge University Press, London Google Scholar
  8. 8.
    Jaubert A. and Marigo J.-J. (2006). Justification of Paris-type fatigue laws from cohesive forces model via a variational approach. Continuum Mech. Thermodyn. V18(1): 23–45 CrossRefMathSciNetGoogle Scholar
  9. 9.
    Achenbach J.D. (1973). Wave Propagation in Elastic Solids. North-Holland, Amsterdam zbMATHGoogle Scholar
  10. 10.
    Truesdell C. and Toupin R. (1960). The classical field theories. In: Flügge, S. (eds) Handbuch der Physik, vol. III/1. Springer, Berlin Google Scholar
  11. 11.
    Griffith A. (1920). The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. A CCXXI-A: 163–198 Google Scholar
  12. 12.
    Freund L.B. (1998). Dynamic Fracture Mechanics, Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, London Google Scholar
  13. 13.
    Bui H.D. (1978). Mécanique de la Rupture Fragile. Masson, Paris Google Scholar
  14. 14.
    Evans L. and Gariepy R. (1992). Measure Theory and Fine Properties of Functions. CRC, Boca Raton zbMATHGoogle Scholar
  15. 15.
    Francfort G.A. and Marigo J.-J. (1998). Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8): 1319–1342 CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    Nguyen Q.S. (2000). Stability and Nonlinear Solid Mechanics. Wiley, London Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut Jean le Rond d’AlembertUniversité Paris VIParisFrance
  2. 2.Laboratoire de Mécanique des SolidesEcole PolytechniqueParisFrance

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