Percolation mechanism of failure of a planar assembly of interlocked osteomorphic elements

A. Molotnikov, Y. Estrin, A. V. Dyskin, E. Pasternak, A. J. Kanel-Belov

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44 Scopus citations


We consider the failure behaviour of a plate assembled from interlocking elements (the so-called osteomorphic blocks) held together by virtue of their geometry and spatial arrangement. As overall failure by crack propagation across the assembly is inhibited by its segmented nature, failure of elements in a random fashion is considered in terms of percolation theory. Overall failure is associated with damage reaching a percolation limit, which is calculated using computer experiments. A new feature of the assembly of interlocked osteomorphic elements as compared to a classical problem of percolation on a square 2-D lattice is the occurrence of avalanches of failures. It is shown that this leads to a significant decrease of the percolation limit, which in our case amounts to about 25% of failed elements. It is further shown that usual scaling laws found in classical percolation theory still apply for the case considered.

Original languageEnglish
Pages (from-to)1222-1232
Number of pages11
JournalEngineering Fracture Mechanics
Issue number8
StatePublished - May 2007
Externally publishedYes

Bibliographical note

Funding Information:
Y.E. acknowledges support through the DFG Grant Es 74/10. A.V.D. and E.P. acknowledge support from the Australian Computational Earth Systems Simulator (ACcESS) – Major National Research Facility. Funding through the Australian Research Council Discovery Grants DP0559737 (A.V.D.) and DP0346148 (E.P.) as well as the ARC Postdoctoral Fellowship (2003–2006) (E.P.) is gratefully acknowledged.


  • Avalanche
  • Cluster
  • Critical exponent
  • Fracture resistance
  • Topological interlocking


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