Crack in a lattice waveguide

We consider some structures where the harmonic ‘feeding’ wave localized at the crack faces can force the crack to grow. First, we present some results related to a lattice with a high-contrast layer, where the wave speed is larger than in the ambient matrix. The analytical solution obtained for the steadystate regime, where the crack speed is independent of the wave amplitude, is used to determine the energy relations and the wave-amplitude-dependent position of the crack front relative to the feeding wave. The corresponding numerical simulations confirmed the existence of the steady-state regime within a range of the wave amplitude. For lager amplitudes the simulations revealed a set of ordered crack-speed oscillation regimes, where the average crack speed is characterized by a stepwise dependence on the wave amplitude. We show that the related cluster-type wave representation allows the average crack speeds to be determined analytically. We also show the connection between the cluster representation and the ‘local’ L. I. Slepyan (B) School of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel e-mail: [email protected] A. B. Movchan Department of Mathematical Sciences, University of Liverpool, Liverpool, UK G. S. Mishuris Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth, UK crack-speeds within the cluster. As an example of a continuous system, where the crack can uniformly grow under the localized harmonic wave, an elastic flexural plate is considered. Both symmetric and antisymmetric fracture modes are examined.