International Journal of Fracture

, Volume 166, Issue 1–2, pp 3–11 | Cite as

On the convergence of 3D free discontinuity models in variational fracture

  • Fernando Fraternali
  • Matteo Negri
  • Michael Ortiz
Original Paper


Free discontinuity problems arising in the variational theory for fracture mechanics are considered. A Γ -convergence proof for an r-adaptive 3D finite element discretization is given in the case of a brittle material. The optimal displacement field, crack pattern and mesh geometry are obtained through a variational procedure that encompasses both mechanical and configurational forces. Possible extensions to cohesive fracture and quasi-static evolutions are discussed.


Variational fracture Free discontinuity models Γ -Convergence r-Adaption Configurational forces 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Fernando Fraternali
    • 1
  • Matteo Negri
    • 2
  • Michael Ortiz
    • 3
  1. 1.Department of Civil EngineeringUniversity of SalernoFisciano, SalernoItaly
  2. 2.Department of MathematicsUniversity of PaviaPaviaItaly
  3. 3.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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