Skip to main content
SpringerLink
Log in

Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics

  • Original Article
  • Published:
Calculus of Variations and Partial Differential Equations Aims and scope Submit manuscript

Abstract

In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Ambrosio L., Fusco N. and Pallara D. (2000). Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York

    Google Scholar 

  2. Bouchitté G., Braides A. and Buttazzo G. (1995). Relaxation results for some free discontinuity problems. J. Reine Angew. Math. 458: 1–18

    MATH  MathSciNet  Google Scholar 

  3. Braides A., Dal Maso G. and Garroni A. (1999). Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case. Arch. Ration. Mech. Anal. 146(1): 23–58

    Article  MATH  MathSciNet  Google Scholar 

  4. Carpinteri A. (1986). Mechanical damage and crack growth in concrete: plastic collapse to brittle fracture. Martinus Nijhoff Publishers, Dordrecht

    MATH  Google Scholar 

  5. Del Piero G. and Truskinovsky L. (1999). A one-dimensional model for lolcalized and distributed fracture. J. Phys. IV 8: 95–102

    Google Scholar 

  6. Del Piero G. and Truskinovsky L. (2001). Macro and micro-cracking in one-dimensional elsticity. Int. J. Solids Struct. 38: 1135–1148

    Article  MATH  Google Scholar 

  7. Truskinovsky L. (1996). Fracture as a phase transition. In: Batra, R.C. and Beatty, M.F. (eds) Contemporary Research in the Mechanics and Mathematics of Materials, pp 322–332. CIMNE, Barcelona

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SISSA, via Beirut 2-4, 34014, Trieste, Italy

    Gianni Dal Maso

  2. Dipartimento di Matematica, Sapienza, Università di Roma, P.le Aldo Moro 3, 00185, Rome, Italy

    Adriana Garroni

Authors
  1. Gianni Dal Maso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adriana Garroni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adriana Garroni.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dal Maso, G., Garroni, A. Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics. Calc. Var. 31, 137–145 (2008). https://doi.org/10.1007/s00526-006-0084-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00526-006-0084-3

Mathematics Subject Classification (2000)

Search

Navigation