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In the present work the steady-state crack propagation in a chain of oscillators with non-local interactions is considered. The interactions are modeled 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.

Most of the research concerting crack propagation in discrete media is concerned with 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 propagating in its 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 solution, and specifically the way the fracture process reaches its steady-state regime. We present the relation between the possible steady-state crack speed and the loading parameters, as well as the energy release rate. In particular, we show that there exists a class of loading regime 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.

Energy dissipation by fast crystalline defects takes place mainly through the resonant interaction of their cores with periodic lattice. We show that the resultant effective friction can be reduced to zero by appropriately tuned acoustic sources located on the boundary of the body. To illustrate the general idea, we consider three prototypical models describing the main types of strongly discrete defects: dislocations, cracks, and domain walls. The obtained control protocols, ensuring dissipation-free mobility of topological defects, can also be used in the design of metamaterial systems aimed at transmitting mechanical information.

The extent to which time-dependent fracture criteria affect the dynamic behavior of fracture in a discrete structure is discussed in this work. The simplest case of a semi-infinite isotropic chain of oscillators has been studied. Two history-dependent criteria are compared to the classical one of threshold elongation for linear bonds. The results show that steadystate regimes can be reached in the low subsonic crack speed range where it is impossible according to the classical criterion. Repercussions in terms of load and crack opening versus velocity are explained in detail. A strong qualitative influence of history-dependent criteria is observed at low subsonic crack velocities, especially in relation to achievable steady-state propagation regimes. Keywords

In the present work the authors revisit a classical problem of crack propagation in a lattice. Authors investigate the questions concerning possible admissible steady-state crack propagations in an anisotropic lattice. It was found that for certain values of contrast in elastic and strength properties of a lattice the stationary crack propagation is impossible. Authors also address a question of possible crack propagation at low velocity.

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Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to propagate at a constant speed along the interface. The choice of the load allows the solution of the problem to be matched with the crack tip field for a Mode III interfacial crack propagating between two dissimilar continuous elastic materials. The lattice problem is reduced to a system of functional equations of the Wiener-Hopf type through the Fourier transform. The derived solution of the system fully characterises the process. We demonstrate the existence of trapped vibration modes that propagate ahead of the crack along the interface during the failure process. In addition, we show as the crack propagates several preferential directions for wave radiation can emerge in the structured medium that are determined by the lattice dissimilarity. The energy attributed to the wave radiation as a result of the fracture process is studied and admissible fracture regimes supported by the structure are identified. The results are illustrated by numerical examples that demonstrate the influence of the dissimilarity of the lattice on the existence of the steady failure modes and the lattice dynamics.