Bifurcation and stability of structures with interacting propagating cracks

Zdeněk P. Bazant*, Mazen R. Tabbara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


A general method to calculate the tangential stiffness matrix of a structure with a system of interacting propagating cracks is presented. With the help of this matrix, the conditions of bifurcation, stability of state and stability of post-bifurcation path are formulated and the need to distinguish between stability of state and stability path is emphasized. The formulation is applied to symmetric bodies with interacting cracks and to a halfspace with parallel equidistant cooling cracks or shrinkage cracks. As examples, specimens with two interacting crack tips are solved numerically. It is found that in all the specimens that exhibit a softening load-displacement diagram and have a constant fracture toughness, the response path corresponding to symmetric propagation of both cracks is unstable and the propagation tends to localize into a single crack tip. This is also true for hardening response if the fracture toughness increases as described by an R-curve. For hardening response and constant fracture toughness, on the other hand, the response path with both cracks propagating symmetrically is stable up to a certain critical crack length, after which snapback occurs. A system of parallel cooling cracks in a halfspace is found to exhibit a bifurcation similar to that in plastic column buckling.

Original languageEnglish (US)
Pages (from-to)273-289
Number of pages17
JournalInternational Journal of Fracture
Issue number3
StatePublished - Feb 1992

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


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