Asymptotic stress intensity factor density profiles for smeared-tip method for cohesive fracture

Zdeněk P. Bažant, Goangseup Zi

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


The paper presents a computational approach and numerical data which facilitate the use of the smeared-tip method for cohesive fracture in large enough structures. In the recently developed K-version of the smeared tip method, the large-size asymptotic profile of the stress intensity factor density along a cohesive crack is considered as a material characteristic, which is uniquely related to the softening stress-displacement law of the cohesive crack. After reviewing the K-version, an accurate and efficient numerical algorithm for the computation of this asymptotic profile is presented. The algorithm is based on solving a singular Abel's integral equation. The profiles corresponding to various typical softening stress-displacement laws of the cohesive crack model are computed, tabulated and plotted. The profiles for a certain range of other typical softening laws can be approximately obtained by interpolation from the tables. Knowing the profile, one can obtain with the smeared-tip method an analytical expression for the large-size solution to fracture problems, including the first two asymptotic terms of the size effect law. Consequently, numerical solutions of the integral equations of the cohesive crack model as well as finite element simulations of the cohesive crack are made superfluous. However, when the fracture process zone is attached to a notch or to the body surface and the cohesive zone ends with a stress jump, the solution is expected to be accurate only for large-enough structures.

Original languageEnglish
Pages (from-to)145-159
Number of pages15
JournalInternational Journal of Fracture
Issue number2
Publication statusPublished - 2003 Jan
Externally publishedYes


  • Asymptotic approximation
  • Cohesive crack
  • Computation
  • Fracture
  • Quasibrittle materials
  • Scaling
  • Size effect
  • Smeared-tip method

ASJC Scopus subject areas

  • Computational Mechanics
  • Modelling and Simulation
  • Mechanics of Materials


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