Analysis of dynamic damage propagation in discrete beam structures

M. J. Nieves, Gennady Mishuris, L. I. Slepyan

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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.
Original languageEnglish
Pages (from-to)699-713
JournalInternational Journal of Solids and Structures
Early online date12 Apr 2016
Publication statusPublished - 15 Oct 2016


  • beam structures
  • waves and fractures
  • discrete media
  • Wiener-Hopf technique


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