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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on January 23, 2008
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbm030
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© The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

DYNAMICS OF A BRIDGED CRACK IN A DISCRETE LATTICE

Gennady S. Mishuris

( Department of Mathematics, Rzeszów University of Technology, Rzeszów, Poland )

Alexander B. Movchan{dagger}

( Department of Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom )

Leonid I. Slepyan

( School of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel )

{dagger} < abm{at}liverpool.ac.uk>

Received 9 April 2007. Revise 18 November 2007.
  Abstract

The paper addresses a problem of partial fracture of a lattice by a propagating fault modelling a crack bridged by elastic fibres. It is assumed that the strength of bonds within the lattice alternates periodically, so that during the dynamic crack propagation only weaker bonds break, whereas the stronger bonds remain intact. The mathematical problem is reduced to the functional equation of the Wiener–Hopf type, which is solved analytically. The load–crack speed dependence is presented, which also has implications on the stability analysis for the bridged crack propagating within the lattice. In particular, we address the evaluation of the dissipation rate, which is found to be strongly dependent on the crack speed. In this lattice model, our results also cover the case of the supercritical crack speed.


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