Dynamics of a bridged crack in a discrete lattice.

MISHURIS, GENNADY S.; MOVCHAN, ALEXANDER B.; SLEPYAN, LEONID I.

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.

FRACTURE mechanics; LATTICE dynamics; LATTICE theory; ELASTIC textiles; FUNCTIONAL equations; WIENER-Hopf equations

Quarterly Journal of Mechanics & Applied Mathematics, 2008, Vol 61, Issue 2, p151

0033-5614

Academic Journal

10.1093/qjmam/hbm030