Journal of Elasticity

, Volume 98, Issue 2, pp 159–187 | Cite as

From Rate-Dependent to Rate-Independent Brittle Crack Propagation

  • Matteo Negri


On the base of many experimental results, e.g., Ravi-Chandar and Knauss (Int. J. Fract. 26:65–80, 1984), Sharon et al. (Phys. Rev. Lett. 76(12):2117–2120, 1996), Hauch and Marder (Int. J. Fract. 90:133–151, 1998), the object of our analysis is a rate-dependent model for the propagation of a crack in brittle materials. Restricting ourselves to the quasi-static framework, our goal is a mathematical study of the evolution equation in the geometries of the ‘Single Edge Notch Tension’ and of the ‘Compact Tension’. Besides existence and uniqueness, emphasis is placed on the regularity of the evolution making reference also to the ‘velocity gap’. The transition to the rate-independent model of Griffith is obtained by time rescaling, proving convergence of the rescaled evolutions and of their energies. Further, the discontinuities of the rate-independent evolution are characterized in terms of unstable points of the free energy. Results are illustrated by a couple of numerical examples in the above mentioned geometries.

Brittle fracture Rate-dependent evolutions Rate-independent evolutions 


62.20.Mm 81.40.Np 

Mathematics Subject Classification (2000)

74R10 74R15 


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

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