International Journal of Fracture

, Volume 199, Issue 2, pp 199–211 | Cite as

Enhanced fictitious crack model accounting for material drawn into the cohesive zone: physically based crack closure criterion

  • Niels Saabye Ottosen
  • Matti Ristinmaa
Original Paper


According to the fictitious crack model, the crack width is infinitely thin at crack initiation and with further loading the crack opens, but no material exists in the cohesive zone. Despite that, the crack is assumed to able to sustain a load. While this is possible at the atomic level, it is not a realistic assumption for the macroscopic behavior we are considering. Invoking the mass conservation law and by postulating a relation between the porosity f of the cohesive zone and the damage variable \(\kappa _{n}\), which is that part of the damage variable \((\kappa )\) that is related to opening of the crack, it is shown that the fictitious crack model can be enhanced so that it accounts for material that is drawn into the cohesive zone. In turn, the amount of material present in the cohesive zone implies a consistent and physically based crack closure criterion. The concepts are first discussed in detail for uniaxial loading and then generalized to arbitrary loadings.


Cohesive zone Mass conservation Crack closure 



Stimulating discussions with Adj. Prof. Johan Tryding, Lund University, Sweden and TetraPak, Lund, Sweden are greatly appreciated.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Division of Solid MechanicsLund UniversityLundSweden

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