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.