Fracture of beams with random field properties: Fractal and Hurst effects

Rossella Laudani, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


The classical problem of peeling a beam off a substrate is studied through a re-examination of Griffith's fracture criterion in the presence of multiscale random properties. Four types of wide-sense homogeneous Gaussian random fields of the vector {Young's modulus E, surface energy density γ}, parametrized by the beam axis, are considered: Ornstein–Uhlenbeck, Matérn, Cauchy, and Dagum. The latter two are multiscale and allow decoupling of the fractal dimension and Hurst effects. Also calculated is the variance of the crack driving force G with any given type of random field in terms of the covariances of E and γ, under either fixed-grip or dead-load conditions. This investigation is complemented by a study of the stochastic crack stability which involves a stochastic competition between potential and surface energies. Overall, we find that, for Cauchy and Dagum models, the introduction of fractal-and-Hurst effects strongly influences the fracture mechanics results. Notably, while the Cauchy and Dagum models represent a more realistic scenario of random fields, given the same covariance on input, the response on output is strongest for Matérn, then Ornstein–Uhlenbeck, then Cauchy and, finally, Dagum model.

Original languageEnglish (US)
Pages (from-to)243-253
Number of pages11
JournalInternational Journal of Solids and Structures
StatePublished - May 15 2020
Externally publishedYes


  • Cauchy random field
  • Dagum random field
  • Fractal
  • Hurst
  • Matérn random field
  • Multiscale random properties
  • Ornstein–Uhlenbeck random field
  • Stochastic fracture

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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