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

doi:10.1016/j.engfracmech.2006.07.012

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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32 Scopus citations

Abstract

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 language	English
Pages (from-to)	1222-1232
Number of pages	11
Journal	Engineering Fracture Mechanics
Volume	74
Issue number	8
DOIs	https://doi.org/10.1016/j.engfracmech.2006.07.012
State	Published - May 2007
Externally published	Yes

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.

Keywords

Avalanche
Cluster
Critical exponent
Fracture resistance
Topological interlocking

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10.1016/j.engfracmech.2006.07.012

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abstract = "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.",

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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. ",

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AU - Kanel-Belov, A. J.

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AB - 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.

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

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Keywords

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