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Spontaneous brittle fracture is studied based on the model of a body, recently introduced by two of the authors, where only the prospective crack path is specified as a discrete set of alternating initially stretched and compressed bonds. In such a structure, a bridged crack destroying initially stretched bonds may propagate under a certain level of the internal energy without external sources. The general analytical solution with the crack speed-energy relation is presented in terms of the crack-related dynamic Green's function. For anisotropic chains and lattices considered earlier in quasi-statics, the dynamic problems are examined and discussed in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. The steady-state sub-and supersonic regimes found analytically are confirmed by numerical simulations. In addition, irregular growth, clustering and crack speed oscillation modes are detected at a lower bound of the internal energy. It is observed, in numerical simulations, that the spontaneous fracture can occur in the form of a pure bridged, partially bridged or fully open crack depending on the internal energy level.
In the last decade, significant theoretical advances were obtained for steady-state fracture propagation in spring-mass lattice structures, that also revealed surprising fracture regimes. Very few articles exist, however, on the dynamic fracture processes in lattices composed of beams. In this paper we analyse a failure (feeding) wave propagating in a beam-made lattice strip with periodically placed point masses. The fracture occurs when the strain of the supporting beam reaches the critical value. The problem reduces to a Wiener-Hopf equation, from which the complete solution is obtained. Two cases are considered when the feeding wave transmits into the intact structure as a sinusoidal wave(s) or only as an evanescent wave. For both cases, a complete analysis of the strain inside the structure is presented. We determine the critical level of the feeding wave, below which the steady-state regime does not exist, and its connections to the feeding wave parameters and the failure wave speed. The accompanied dynamic effects are also discussed. Amongst much else, we show that the switch between the two considered regimes introduces a rapid change in the minimum energy required for the failure wave to propagate steadily. The failure wave developing under an incident sinusoidal wave is remarkable due to the fact that there is an upper bound of the domain where the steady-state regime exists. In the present paper, only the latter is examined; the alternative regimes are considered separately.
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