Dynamic fracture of a discrete media under moving load

Most of the research concerning crack propagation in discrete media is carried out for specific types of external loading: displacements on the boundaries, or constant energy fluxes or feeding waves originating from infinity. In this paper the action of a moving load is analysed on the simplest lattice model: a thin strip, where the fault propagates in the middle portion as the result of the moving force acting on the destroyed part of the structure. We study both analytically and numerically how the load amplitude and its velocity influence the possible solutions, and specifically the way the fracture process reaches its steady-state regimes. We present the relation between the possible steady-state crack speeds and the loading parameters, as well as the energy release rate. In particular, we show that there exists a class of loading regimes corresponding to each point on the energy-speed diagram (and thus determine the same limiting steady-state regime). The phenomenon of the ”forbidden regimes” is discussed in detail, from both the points of view of force and energy. For a sufficiently anisotropic structure, we find a stable steady-state propagation corresponding to the ”slow” crack. Numerical simulations reveal various ways by which the process approaches - or fails to approach - the steady-state regime. The results extend our understanding of fracture processes in discrete structures, and reveal some new questions that should be addressed.