Enhanced resistance of mode II fracture by nonlocal interactions in 2D locally resonant elastic wave metamaterials

As a significant extension of classical structures, elastic wave metamaterials are widely applied to the vibration isolation and turning wave propagation. However, little attention has been paid on their fracture and arrest properties. In this work, the dispersion curves and arrest property of mode II crack in 2D elastic wave metamaterials are studied, in which both nonlocal interactions and local resonators are considered. Because every unit cell is connected to the second nearest neighboring one with the massless spring along the x-direction, the nonlocal interaction is achieved. The dynamic effective mass is derived and influences of nonlocal interactions on the dispersion relation are analyzed. Moreover, the energy release ratio which characterizes the arrest ability is derived and the effects of structural parameters are discussed. The theoretical predictions are also compared to the finite element simulation. Numerical results show that the crack propagation resistance of mode II crack can be improved significantly by introducing proper nonlocal springs within a finite steady-state region. But in the oscillation region, the energy release ratio G0/G is unstable. Furthermore, an additional energy barrier can be generated before the region in which the crack propagates stably.