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: • re the conditions of existence of the localised knife wave? s the lower bound of the amplitude of the feeding wave, which supports the crack propagation, for a given deformational fracture criterion? es the crack speed depend on the amplitude of the feeding wave? re the dissipative waves? How much energy is irradiated by these waves and what is the total dissipation? re the conditions of existence of the steady-state regime for the propagating crack? sider 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.