Dynamics of a bridged crack in a discrete lattice

Gennady S. Mishuris, Alexander B. Movchan*, Leonid I. Slepyan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)151-160
Number of pages10
JournalQuarterly Journal of Mechanics and Applied Mathematics
Issue number2
StatePublished - May 2008


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