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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. [ABSTRACT FROM AUTHOR]

In the present work, the steady-state crack propagation in a chain of oscillators with non-local interactions is considered. The interactions are modelled as linear springs, while the crack is presented by the absence of extra springs. The problem is reduced to the Wiener-Hopf type, and solution is presented in terms of the inverse Fourier transform. It is shown that the non-local interactions may change the structure of the solution well known from the classical local interactions formulation. In particular, it may change the range of the region of stable crack motion. The conclusions of the analysis are supported by numerical results. Namely, the observed phenomenon is partially clarified by evaluation of the structure profiles on the crack line ahead. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A model for crack propagation along a non-locally pre-stressed interface in ceramic materials is studied. The problem is analysed on a discrete chain of oscillators, with local and non-local interactions. The pre-stressed state is defined by the stiffnesses of the non-local links. Small negative stiffnesses of such links reveals the existence of crack speeds supporting stable crack propagation, which is not possible in a structure which has only local interactions. [ABSTRACT FROM AUTHOR]