Localised knife waves in a structured interface

We consider a Mode III lattice with an interface layer where the dynamic crack growth is caused by a localised sinusoidal wave. In the wave-fracture scenario, the 'feeding wave' (here also called the knife wave) delivers energy to the moving crack front, while the dissipative waves carry a part of this energy away from the front. The questions addressed here are: What are the conditions of existence of the localised knife wave? What is the lower bound of the amplitude of the feeding wave, which supports the crack propagation, for a given deformational fracture criterion? How does the crack speed depend on the amplitude of the feeding wave? What are the dissipative waves? How much energy is irradiated by these waves and what is the total dissipation? What are the conditions of existence of the steady-state regime for the propagating crack? We consider analytically two established regimes: the steady-state regime, where the motion of neighbouring masses (along the interface) differs only by a constant shift in time, and an alternating-strain regime, where the corresponding amplitudes differ by sign. We also present the numerical simulation results for a model of a high-contrast interface structure. Along with the energy of the feeding and dissipative waves, an energy radiated to the bulk of the lattice is identified. (c) 2009 Elsevier Ltd. All rights reserved.