Archive for Rational Mechanics and Analysis

, Volume 228, Issue 3, pp 867–889 | Cite as

Approximation of a Brittle Fracture Energy with a Constraint of Non-interpenetration

  • Antonin Chambolle
  • Sergio Conti
  • Gilles A. Francfort


Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over an SBD type space. The corresponding functional can in turn be approximated in the sense of \({\Gamma}\)-convergence by a sequence of functionals involving a phase field as well as the displacement field. We show that a similar approximation persists if additionally imposing a non-interpenetration constraint in the minimization, namely that only nonnegative normal jumps should be permissible.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.CMAP, Ecole PolytechniqueCNRSPalaiseau CedexFrance
  2. 2.Institut für Angewandte MathematikUniversität BonnBonnGermany
  3. 3.LAGA, Université Paris-NordVilletaneuseFrance
  4. 4.Courant InstituteNew YorkUSA

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