Brittle fracture in a periodic structure with internal potential energy. Spontaneous crack propagation

Mark Ayzenberg-Stepanenko, Gennady Mishuris, Leonid Slepyan

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Spontaneous brittle fracture is studied based on the model of a body, recently introduced by two of the authors, where only the prospective crack path is specified as a discrete set of alternating initially stretched and compressed bonds. In such a structure, a bridged crack destroying initially stretched bonds may propagate under a certain level of the internal energy without external sources. The general analytical solution with the crack speed-energy relation is presented in terms of the crack-related dynamic Green's function. For anisotropic chains and lattices considered earlier in quasi-statics, the dynamic problems are examined and discussed in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. The steady-state sub- and supersonic regimes found analytically are confirmed by numerical simulations. In addition, irregular growth, clustering and crack speed oscillation modes are detected at a lower bound of the internal energy. It is observed, in numerical simulations, that the spontaneous fracture can occur in the form of a pure bridged, partially bridged or fully open crack depending on the internal energy level.

Original languageEnglish
Article number20140121
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2167
StatePublished - 8 Jul 2014
Externally publishedYes


  • Dynamic fracture
  • Failure waves
  • Periodic structure

ASJC Scopus subject areas

  • Mathematics (all)
  • Engineering (all)
  • Physics and Astronomy (all)


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