Crack in a lattice waveguide

摘要

We consider some structures where theharmonic 'feeding' wave localized at the crack facescan force the crack to grow. First, we present someresults related to a lattice with a high-contrast layer,where the wave speed is larger than in the ambientmatrix. The analytical solution obtained for the steady-state regime, where the crack speed is independentof the wave amplitude, is used to determine theenergy relations and the wave-amplitude-dependentposition of the crack front relative to the feedingwave. The corresponding numerical simulations con-firmed the existence of the steady-state regime within arange of the wave amplitude. For lager amplitudes thesimulations revealed a set of ordered crack-speedoscillation regimes, where the average crack speed ischaracterized by a stepwise dependence on the waveamplitude. We show that the related cluster-type waverepresentation allows the average crack speeds to bedetermined analytically. We also show the connec-tion between the cluster representation and the ‘local'crack-speeds within the cluster. As an example of acontinuous system, where the crack can uniformlygrow under the localized harmonic wave, an elasticflexural plate is considered. Both symmetric and anti-symmetric fracture modes are examined.